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TAMAVAQ/Q-TAMAVAQ: An Audit-First Quantum-Geometric Framework for Reproducible Neoantigen Panel Triage in Glioma

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21 July 2026

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21 July 2026

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Abstract
Personalized glioma neoantigen vaccination requires a defensible way to prioritize candidate peptides when mutation, HLA presentation, biochemical, structural, manufacturability, and provenance signals are incomplete or discordant. We present TAMAVAQ/Q-TAMAVAQ, an audit-first computational framework that converts candidate triage from an opaque rank list into a replayable constrained decision process. Candidate dossiers are embedded with a Fubini-Study-style fidelity kernel, connected through a symmetrized 12-nearest-neighbour graph, and assigned CTQW neighborhood support. A deterministic MBHA boundary ledger records signed eligibility margins and preserves non-compensatory BIO, PHYS, GEOM, CMC, PROV, and VALID requirements. In the internal worksheet described in the source manuscript, the analysis contains n = 1,537 candidate records and a locked 65-candidate evidence-positive endpoint (4.23%). The full selector achieved AP = 0.552, AUROC = 0.962, and NDCG@100 = 0.693, compared with AP = 0.505 for graph-transport support alone and AP = 0.515 for a non-graph linear comparator. These findings establish internal computational feasibility and auditability only; biological validation remains prospective. The final proof schematic consolidates the quantum geometry, CTQW transport, PASS oracle and MBHA margin ledger into a single theorem-linked audit description.
Keywords: 
glioma
;  
neoantigen prioritization
;  
auditability
;  
graph transport
;  
CTQW
;  
Fubini-Study kernel
;  
HLA-balanced peptide panel
;  
mathematical chemistry
;  
original research article
Subject: 
Biology and Life Sciences  -   Biophysics
Significance Statement. Personalized neoantigen vaccination requires evidence integration without hiding why a candidate passes or fails. TAMAVAQ/Q-TAMAVAQ formalizes this task as a replayable ledger that joins calibrated biological evidence, structural chemistry, Fubini-Study-style graph geometry, continuous-time quantum-walk (CTQW) support, and a deterministic MBHA boundary mask. The framework is computational and audit-first: it does not assert biological quantum coherence, hardware quantum advantage, animal efficacy, or clinical benefit. Its value is a transparent, HLA-balanced certificate and a fixed record of selected, reserve, and failed candidates.

List of main equations

Table 1. Main mathematical and chemical equations used in the research article. The notation consolidates the candidate ledger, calibrated BIO field, non-compensatory gates, thermodynamic mapping, Fubini-Study geometry, CTQW transport, MBHA boundary score, replay hash, patient expression evidence and prospective CD4/CD8 assay endpoint. Detailed derivations correspond to SI Appendix I equation blocks S1.0.1-S1.0.16 and S1.M1-S1.M22 and SI Appendix II equations S.E1-S.E36.
Table 1. Main mathematical and chemical equations used in the research article. The notation consolidates the candidate ledger, calibrated BIO field, non-compensatory gates, thermodynamic mapping, Fubini-Study geometry, CTQW transport, MBHA boundary score, replay hash, patient expression evidence and prospective CD4/CD8 assay endpoint. Detailed derivations correspond to SI Appendix I equation blocks S1.0.1-S1.0.16 and S1.M1-S1.M22 and SI Appendix II equations S.E1-S.E36.
No. Object Mathematical-physics notation
E1 Candidate dossier vector x_i=(sequence_i,HLA_i,BIO_i,ΔG_i,CP_i,RMSD_i*,RMSF_i*,GEOM_i,CMC_i,PROV_i,VALID_i)^T
E2 BIO calibration BIO_i=C_BIO(s_i)=σ(a s_i+b), σ(u)=(1+e^{-u})^{-1}
E3 Signed predicate margin b_ir=z_ir-τ_r
E4 Non-compensatory pass mask PASS_i=Π_r H(b_ir), r∈{BIO,PHYS,GEOM,CMC,PROV,VALID}
E5 Thermodynamic mapping ΔG°=RT ln K_d, K_d=exp(ΔG°/RT)
E6 Normalized descriptor state |ψ_i⟩=x_i/||x_i||_2
E7 Fidelity kernel K_ij=|⟨ψ_i|ψ_j⟩|^2
E8 Fubini-Study-style distance d_FS(i,j)=arccos(√K_ij)
E9 Heat-kernel graph weight W_ij=exp[-d_FS(i,j)^2/σ^2]
E10 Graph Laplacian D_ii=Σ_j W_ij, L=D-W
E11 CTQW propagator U(t)=exp(-itL)
E12 Transported support p_i(t)=|⟨i|U(t)|ψ_0⟩|^2, Σ_i p_i(t)=1
E13 Predicate oracle O_PASS|i⟩=(-1)^{PASS_i}|i⟩
E14 Boundary score S_MBHA(i)=S_base(i)+λ_Tp_i(t)+λ_BΣ_r w_r tanh(b_ir/s_r)-λ_R redun_i
E15 Certified score S_cert(i)=PASS_i S_MBHA(i)
E16 Replay digest H_batch=SHA256(D||C_BIO||τ||G||t||w||Φ||F||k)
E17 Patient expression-weighted evidence E_p=log_2(FPKM_p+1)max(NAF_p^DNA,NAF_p^RNA)
E18 HLA compatibility indicator A(p,h)=1[HLA_p=h and h∈G_patient]
E19 Superiority criterion Superior(M)=1[AP_M>AP_comp ∧ NDCG_M>NDCG_comp ∧ Audit_M=1]
E20 Prospective assay endpoint Y_CD4CD8CXP=ranked abundance of CD4/CD8 composite events across prespecified peptide pools

Introduction

Glioblastoma and related glioma settings present a difficult neoantigen-design problem because the evidence for any candidate peptide is distributed across mutational context, expression, HLA presentation, peptide chemistry, structural plausibility, synthesis feasibility and provenance. A method that merely sorts by one predicted affinity can obscure why a candidate is retained, which candidate should remain as reserve, and which mandatory requirement failed. The present framework treats selection as a declared operator over an immutable candidate ledger rather than as a narrative shortlist [53,54,55,56,57,72,73,74,75,76,77,79,80,81,82,83,84,85,86,87,88,89,90].
TAMAVAQ/Q-TAMAVAQ is therefore positioned as an audit and constraint layer. It remains compatible with NetMHC-family predictors, MHCflurry, pVACtools, CEDAR/IEDB-style resources, IMPROVE-type immunogenicity logic, structure prediction, docking, and molecular simulation. The contribution is not to replace those tools, but to wrap their outputs in a transparent decision grammar with threshold vectors, signed margins, graph support, deterministic replay and explicit claim boundaries [1,11,49,50,51,52,53,54,55,56,57,58,59,60,61,68,69,70,71,72,73,74,75,76,77].
The manuscript preserves a strict distinction between computational support and biological validation. CTQW is used as a graph-neighborhood transport calculation on a descriptor graph; it is not presented as evidence that tumor tissue, peptides or lymphocytes maintain biological quantum coherence. Similarly, the MBHA vocabulary is used as a boundary ledger for signed margins and reserve semantics, not as a physical cosmology claim. This claim discipline follows the SI Appendix I and II records that define the replay contract, operator register and validation boundary.

Supporting Information Architecture

Table 2. Supplementary information architecture. SI Appendix I and SI Appendix II define the equations, tables, figure panels, replay state, ablation controls and claim-boundary records used throughout the article.
Table 2. Supplementary information architecture. SI Appendix I and SI Appendix II define the equations, tables, figure panels, replay state, ablation controls and claim-boundary records used throughout the article.
Register Items Main-text role Scientific function
SI Appendix I Figs. S1-S6; Tables S1-S24; equations S1.0.1-S1.0.16 Introduction, Methods, Fig. 1 Audit circuit, predicate registers, threshold vectors, replay manifest and FS/CTQW diagnostics.
SI Appendix I Figs. S7-S12; Tables S25-S89 Results, chemical/biological data, prospective validation boundary Structural-interface dashboards, peptide-level chemistry, sequence/property controls and prospective assay design.
SI Appendix I Figs. S13-S28i; Tables S90-S93 Proofs, discussion and conclusion Mathematical-chemistry proof chain, MBHA boundary geometry, claim-control and manifest summaries.
SI Appendix II Equations S.E1-S.E36; Figs. SII1-SII13; Tables SII1-SII11 and SII6a Operator and replay verification Independent kernel construction, oracle decomposition, boundary-ledger verification and claim-boundary checks.

Audit-First Workflow and Predicate Construction

The full pipeline begins with candidate dossiers containing sequence, HLA, calibrated biological support, structural chemistry, manufacturability, provenance and validation state. Each dossier is normalized into a mathematical descriptor state and evaluated against non-compensatory gates. The workflow in Figure 1 summarizes this progression from candidate evidence to HLA-balanced certificate.
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Figure 1. Audit-first quantum-geometric triage workflow for glioma neoantigen prioritization. The figure integrates candidate dossier loading, BIO/PHYS/GEOM/CMC/PROV/VALID gates, the Fubini-Study-style 12-nearest-neighbour graph, CTQW support, deterministic MBHA boundary ledger, HLA-balanced certificate logic and claim-boundary reproducibility. SI Appendix I Tables S1-S12 and SI Appendix II equations S.E1-S.E12 provide the threshold and replay records.
Figure 1. Audit-first quantum-geometric triage workflow for glioma neoantigen prioritization. The figure integrates candidate dossier loading, BIO/PHYS/GEOM/CMC/PROV/VALID gates, the Fubini-Study-style 12-nearest-neighbour graph, CTQW support, deterministic MBHA boundary ledger, HLA-balanced certificate logic and claim-boundary reproducibility. SI Appendix I Tables S1-S12 and SI Appendix II equations S.E1-S.E12 provide the threshold and replay records.
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Results

Non-Compensatory Gates Preserve Explicit Eligibility

Every candidate must pass all mandatory predicates before selection or reserve assignment. The BIO gate requires calibrated biological support, the PHYS gate requires structural/energetic consistency, the GEOM gate requires graph-supported coherence, and CMC/PROV/VALID enforce feasibility, traceability and validation-state completeness. This prevents compensatory promotion: a strong CTQW neighborhood support term cannot rescue a record with missing provenance, failed manufacturability or inadequate biological calibration [49,50,51,52,70,71].
Table 3. Predicate architecture used to compute PASS. The table expands the main gate logic while retaining the same order used in SI Appendix I and SI Appendix II.
Table 3. Predicate architecture used to compute PASS. The table expands the main gate logic while retaining the same order used in SI Appendix I and SI Appendix II.
Gate Main rule Interpretation SI support
BIO BIO_i >= 0.70 after calibration Presentation, processing, expression and immunogenicity support must be sufficient. SI Appendix I S1.0.1-S1.0.16; SI Appendix II S.E5-S.E8
PHYS ΔG, CP, RMSD* and RMSF* subgates pass Physical feasibility is a conjunction of energetic and conformational checks. SI Appendix I Tables S7-S10 and S25-S28
GEOM GEOM_i >= 0.75 Candidate lies within graph-supported evidence neighborhood. SI Appendix I Tables S13-S24; SI Appendix II S.E13-S.E18
CMC Manufacturability admissible Synthesis and handling risks are visible before panel certification. SI Appendix I Tables S3-S12
PROV/VALID Source, version and validation state present Untraceable or state-incomplete records are not certified. SI Appendix I Tables S90-S93; SI Appendix II SII6-SII6a
PASS product of all mandatory gate bits Only PASS candidates can be selected or used as reserves. SI Appendix II Tables SII1-SII6a

Figure 2 overview atlas and database-scale benchmark

The integrated Figure 2 overview atlas combines prospective CD4/CD8 flow-cytometry design strata, peptide-pool mapping, quantum-circuit audit logic, structural and energetic summaries, benchmark comparisons and numerical quantum scoring. The atlas functions as a compact visual map linking the deterministic computational ledger to prospective assay strata; it is not interpreted as completed wet-lab validation.
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Figure 2. In vitro CD4/CD8 validation atlas, peptide pools and quantum-circuit audit layer. The integrated atlas summarizes flow-cytometry strata, peptide-pool logic, structural and energetic links, individualized circuit instantiation, quantum-score benchmarking, selected/reserve peptide scoring and reference crosswalk. The flow-cytometry panels define prospective assay design rather than observed experimental evidence. SI Appendix I Tables S13-S89 and SI Appendix II equations S.E1-S.E36 provide the corresponding sequence, graph, boundary, replay and claim-control records.
Figure 2. In vitro CD4/CD8 validation atlas, peptide pools and quantum-circuit audit layer. The integrated atlas summarizes flow-cytometry strata, peptide-pool logic, structural and energetic links, individualized circuit instantiation, quantum-score benchmarking, selected/reserve peptide scoring and reference crosswalk. The flow-cytometry panels define prospective assay design rather than observed experimental evidence. SI Appendix I Tables S13-S89 and SI Appendix II equations S.E1-S.E36 provide the corresponding sequence, graph, boundary, replay and claim-control records.
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Quantitative Benchmark and Quantum-Score Analysis

The internal benchmark evaluates fixed selectors against a locked evidence-positive endpoint. Because endpoint labels and derivatives are withheld from preprocessing, feature construction, graph construction, CTQW initialization, score coefficients, gate margins and panel constraints, the numerical comparison is interpreted as a replay-controlled computational proof of concept rather than a clinical validation claim. The resulting performance pattern favours the full selector: graph transport contributes support, but the full FS-CTQW-MBHA gate-and-ledger system gives the highest combined audit and ranking performance [1,11,49,50,51,52,62,63,64,65,66,67,70,71].
Table 4. Quantum-score benchmark and method comparison. TAMAVAQ/Q-TAMAVAQ is highlighted because it jointly preserves non-compensatory gates, CTQW graph support, boundary audit and replay feasibility. The AP, AUROC and NDCG values are the internal computational benchmark values reported in the attached manuscript and summarized in SI Appendix I comparator and replay records.
Table 4. Quantum-score benchmark and method comparison. TAMAVAQ/Q-TAMAVAQ is highlighted because it jointly preserves non-compensatory gates, CTQW graph support, boundary audit and replay feasibility. The AP, AUROC and NDCG values are the internal computational benchmark values reported in the attached manuscript and summarized in SI Appendix I comparator and replay records.
Method AP AUROC NDCG@100 Top-1 recall Calibration RMSE Composite Q-score
TAMAVAQ/Q-TAMAVAQ 0.552 0.962 0.693 0.92 0.12 0.87
Graph-transport only 0.505 0.901 0.641 0.81 0.21 0.67
Linear comparator 0.515 0.914 0.652 0.83 0.19 0.71
NetMHCpan-style baseline 0.463 0.872 0.598 0.72 0.28 0.58
pVACtools-style baseline 0.447 0.861 0.581 0.69 0.31 0.54
Binding-only control 0.198 - 0.271 2/4 PASS hits - single stream
Immunogenicity-only control 0.075 - 0.063 incomplete - single stream
Table 5. Numerical quantum scoring analysis of selected and reserve peptides. C01-C04 fill the selected boundary; C05-C07 remain positive-margin reserves. The table mirrors the selected/reserve logic in Figure 2 and the boundary-ledger fields in SI Appendix II Table SII6a.
Table 5. Numerical quantum scoring analysis of selected and reserve peptides. C01-C04 fill the selected boundary; C05-C07 remain positive-margin reserves. The table mirrors the selected/reserve logic in Figure 2 and the boundary-ledger fields in SI Appendix II Table SII6a.
Candidate CTQW support p_i(t) GEOM score MBHA score Boundary margin Γ_i Final state
C01 0.91 0.93 0.92 +0.18 Selected
C02 0.88 0.90 0.88 +0.14 Selected
C03 0.85 0.88 0.85 +0.10 Selected
C04 0.82 0.86 0.83 +0.06 Selected
C05 0.79 0.82 0.79 +0.04 Reserve
C06 0.76 0.80 0.76 +0.03 Reserve
C07 0.74 0.78 0.74 +0.02 Reserve

HLA-Balanced Certificate and Patient-Specific Validation Bridge

Figure 3 presents the patient-specific register and prospective validation bridge. It combines the HLA-balanced 24-peptide certificate logic, selected/reserve register, patient-specific neoepitope inputs and prospective validation chain from synthesis/QC through HLA-pMHC testing, cellular assays and future GL261-luc2 design. The claim boundary is explicit: no survival, tumor-control, PET/MRI, FCS, cytokine or clinical outcomes are reported in this article.
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Figure 3. HLA-balanced certificate, patient-specific register and prospective validation bridge. The figure aligns the selected/reserve register with allele-matched peptide assignments and future assay steps. It defines a prospective design bridge rather than an observed-result figure. Extended patient-specific and assay-design logic is provided in SI Appendix I Tables S41-S89 and SI Appendix II replay equations.
Figure 3. HLA-balanced certificate, patient-specific register and prospective validation bridge. The figure aligns the selected/reserve register with allele-matched peptide assignments and future assay steps. It defines a prospective design bridge rather than an observed-result figure. Extended patient-specific and assay-design logic is provided in SI Appendix I Tables S41-S89 and SI Appendix II replay equations.
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Table 6. Compact selected/reserve peptide ledger. The table links the long-anchor record with allele-matched short partners and reserve peptides. Extended chemistry descriptors, motif/logo evidence, HLA mapping, docking/MD dashboards and peptide QC records are in SI Appendix I Tables S13-S49.
Table 6. Compact selected/reserve peptide ledger. The table links the long-anchor record with allele-matched short partners and reserve peptides. Extended chemistry descriptors, motif/logo evidence, HLA mapping, docking/MD dashboards and peptide QC records are in SI Appendix I Tables S13-S49.
ID Exact sequence Length HLA/register State Role
C01 TLWYDRPMYVSTTIFLV 17 long-anchor selected anchor peptide
C02 ILCEKPTVTTV 11 HLA-A*02:01 selected allele-matched short partner
C03 EESYDFFKSY 10 HLA-A*26:01 selected allele-matched short partner
C04 IDESPIFKEF 10 HLA-B*18:01 selected allele-matched short partner
C05 LPGGSYMAKF 10 HLA-B*35:01 reserve reserve peptide
C06 SFDNNIIKM 9 HLA-C*04:01 reserve reserve peptide
C07 LRSQVRAIY 9 HLA-C*07:01 reserve reserve-shell record
Table 7. Patient-specific neoepitope input layer. DNA NAF, RNA NAF, FPKM and HLA restriction are retained as explicit variables in the patient-specific evidence state. Class-II records without concrete peptide windows remain prospective until a final sequence and processing state are enumerated.
Table 7. Patient-specific neoepitope input layer. DNA NAF, RNA NAF, FPKM and HLA restriction are retained as explicit variables in the patient-specific evidence state. Class-II records without concrete peptide windows remain prospective until a final sequence and processing state are enumerated.
No. Peptide Gene / coding information DNA NAF RNA NAF FPKM HLA allele/class
1 STSPPGTRV TP53:NM_000546:c.C180T:p.P90S 0.48 0.67 25.78 HLA-A*02:01
2 TLFNLLSARY HEATR1:NM_018072.5:c.C3725T:p.R1235C 0.31 0.35 1.93 HLA-C*07:01
3 VSNRYYLTPFTL MRPS15:NM_031280:c.A303G:p.P101T 0.26 0.37 51.42 HLA-C*07:01
4 TFQFTPYSWVR PTDSS2:NM_030783:c.G874A:p.A292T 0.17 0.11 11.39 HLA-A*02:01
5 RLHELPKMNC SPAG16:NM_024532:c.A1200T:p.E400V 0.52 0.22 19.69 HLA-C*07:01
6 HREKSGGPG XPC:NM_004628:c.G1517C:p.R506G 0.17 0.19 3.76 HLA-A*02:01
7 GSTIDCNRLF not specified in source table 0.13 0.25 4.95 HLA-A*02:01
8 Class-II window pending IDH1:NM_005896:c.G395T:p.R132C 0.27 0.43 132.39 Class II
9 TRQQKREYSRKMAAGM SLIT2:NM_004787:c.A300G:p.I100Y 0.45 0.69 21.68 Class II
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Figure 4. Modified black-hole margin-boundary neoantigen selector with CTQW-Fubini-Study circuit audit. The panel uses enlarged inter-element margins and a constrained subpanel grid to emphasize the deterministic MBHA boundary layer as a selected/reserve/fail margin operator. Evidence-state dossiers are converted into Fubini-Study-style geometry, transported through a symmetrized 12-nearest-neighbour Laplacian CTQW support term, predicate-marked by the non-compensatory PASS oracle and emitted as a bounded MBHA score ledger. Numerical callouts summarize n = 1,537 candidates, 65 endpoint positives (4.23%), graph bandwidth sigma = 0.03892, CTQW time t = 0.25, AP = 0.552, AUROC = 0.962, Delta4 = 0.040 and the 24-peptide HLA-balanced certificate. The schematic is a quantum-communications-style audit abstraction, not a claim of biological quantum coherence or clinical efficacy; detailed values and theorem registers are provided in SI Appendices I and II.
Figure 4. Modified black-hole margin-boundary neoantigen selector with CTQW-Fubini-Study circuit audit. The panel uses enlarged inter-element margins and a constrained subpanel grid to emphasize the deterministic MBHA boundary layer as a selected/reserve/fail margin operator. Evidence-state dossiers are converted into Fubini-Study-style geometry, transported through a symmetrized 12-nearest-neighbour Laplacian CTQW support term, predicate-marked by the non-compensatory PASS oracle and emitted as a bounded MBHA score ledger. Numerical callouts summarize n = 1,537 candidates, 65 endpoint positives (4.23%), graph bandwidth sigma = 0.03892, CTQW time t = 0.25, AP = 0.552, AUROC = 0.962, Delta4 = 0.040 and the 24-peptide HLA-balanced certificate. The schematic is a quantum-communications-style audit abstraction, not a claim of biological quantum coherence or clinical efficacy; detailed values and theorem registers are provided in SI Appendices I and II.
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Mathematical Chemistry Proof Obligations

The proofs below are computational and mathematical. They establish bounded geometry, probability conservation, non-compensatory exclusion and replay determinism. They do not assert biological efficacy, hardware speedup, or clinical outcome. This proof style follows the mathematical-chemistry registers in SI Appendix I and the independent replay equations in SI Appendix II.
0 <= K_ij = |<psi_i, psi_j>|^2 <= 1, 0 <= d_FS(i,j)=arccos(sqrt(K_ij)) <= pi/2
Bounded Fubini-Study support follows from normalization and Cauchy-Schwarz. The arccosine map sends the square-root fidelity to a real angular distance. Heat-kernel edges are non-negative and the symmetrized graph gives a real symmetric W, so L = D - W is positive semidefinite under the usual quadratic form [62,63,64,65,66,67].
v^T L v = 1/2 sum_{i,j} W_ij (v_i-v_j)^2 >= 0, U(t)=exp(-itL)
Because L is real symmetric, -iL is skew-Hermitian and U(t) is unitary. The transported support vector p_i(t) therefore conserves probability. This makes CTQW a support redistribution on the descriptor graph rather than a source of evidence that can replace mandatory biological or chemical gates.
U(t)^† U(t)=I, p_i(t)=|<i|U(t)|psi_0>|^2, sum_i p_i(t)=1
The non-compensatory proof is immediate from the multiplicative PASS mask. If any required gate is zero, the product is zero and the certified score becomes zero regardless of graph support, docking score, sequence convenience or rank position. The design explicitly prevents a high value in one channel from erasing a failed mandatory requirement [49,50,51,52,70,71].
PASS_i=g_i^BIO g_i^PHYS g_i^GEOM g_i^CMC g_i^PROV g_i^VALID, S_cert(i)=PASS_i S_MBHA(i)
The replay proof fixes the ordered candidate ledger, calibration object, threshold vector, graph, propagation time, score weights, oracle definition, panel feasibility policy and panel depth. Any change to peptide sequence, threshold, score, graph bandwidth, propagation time, weight or policy changes the replay digest and creates a new state rather than a hidden rerun.
H_batch = SHA256(D || C_BIO || tau || G || t || w || Phi || F || k)

Thermodynamic and Biological Interpretation

The PHYS block is interpreted using unit-aware chemical reasoning. Docking, molecular dynamics and contact persistence are physical descriptors unless calibrated to measured thermodynamics. When thermodynamic mapping is used, standard free energy and dissociation constant are reported with explicit units and temperature assumptions. A low docking score alone is not treated as proof of biological activity; it must align with contact persistence, RMSD*, RMSF*, BIO calibration and the full PASS predicate [58,59,60,61,68,69].
Delta G^0 = RT ln K_d, K_d = exp(Delta G^0/RT)
Biological calibration is similarly separated from discrimination. Presentation, processing, expression, clonality and immunogenicity features can feed the BIO score, but the calibrated support value must be versioned and thresholded before oracle marking. This separation keeps the evidence auditable and prevents a discriminative but uncalibrated predictor from becoming an undocumented probability claim [53,54,55,56,57,70,71,73,74,75,76,77].
BIO_patient(p)=sigma(beta_0 + beta_1 E_p + beta_2 A(p,h) + beta_3 processing(p) + beta_4 motif(p))
For patient-specific records, expression-weighted evidence E_p = log2(FPKM+1) max(NAF^DNA, NAF^RNA) supplies an auditable prior rather than a presentation proof. HLA compatibility A(p,h) then restricts the candidate to the patient genotype, after which BIO, PHYS, GEOM, CMC, PROV and VALID gates remain mandatory. This logic is especially important in glioma, where candidate scarcity must not weaken proof standards [72,79,80,81,82,83,86,87,88,89,90].
Table 8. Blood-derived HLA genotype and allele-matched peptide assignments. These six presentation axes define the patient-specific class-I register while preserving the same PASS, CTQW and MBHA replay logic used in the fixed reference analysis.
Table 8. Blood-derived HLA genotype and allele-matched peptide assignments. These six presentation axes define the patient-specific class-I register while preserving the same PASS, CTQW and MBHA replay logic used in the fixed reference analysis.
Blood-derived HLA allele Assigned peptide Use in personalized pool
HLA-C*07:01 LRSQVRAIY Allele-matched short partner
HLA-C*04:01 SFDNNIIKM Allele-matched short partner
HLA-B*35:01 LPGGSYMAKF Allele-matched short partner
HLA-B*18:01 IDESPIFKEF Allele-matched short partner
HLA-A*26:01 EESYDFFKSY Allele-matched short partner
HLA-A*02:01 ILCEKPTVTTV Allele-matched short partner

Methods

Candidate Loading and Graph Construction

Candidate inclusion required a syntactically valid peptide sequence, a stable identifier, HLA context when available, calibrated BIO support, structural and physical descriptors, manufacturability, provenance and validation-state fields. Failed records remain visible as FAIL rather than being silently discarded. Dossier vectors were scaled and normalized before computing the fidelity kernel and 12-nearest-neighbour graph. Endpoint labels were withheld from preprocessing, graph construction, score coefficients, boundary margins and panel policy [1,11,49,50,51,52,70,71].
The graph Laplacian acts as the transport operator. The calculation is executed as a classical graph-transport support score with quantum-walk notation. The phase oracle marks only PASS candidates, and final certificate emission remains classical and constrained by HLA balance, sequence distinctness and reserve accounting. This gives an inspectable oracle and reproducible boundary ledger without claiming hardware quantum advantage [62,63,64,65,66,67].

Ablation, Replay and Claim Control

Table 9. Circuit ablation and reproducibility checks. Removal or perturbation of BIO, PHYS, FS/CTQW or MBHA modules is assessed by PASS changes, physical descriptor sensitivity, transport-prior shifts and replay mismatch. The prospective flow-cytometry atlas is not an observed verification readout.
Table 9. Circuit ablation and reproducibility checks. Removal or perturbation of BIO, PHYS, FS/CTQW or MBHA modules is assessed by PASS changes, physical descriptor sensitivity, transport-prior shifts and replay mismatch. The prospective flow-cytometry atlas is not an observed verification readout.
Module removed or perturbed Expected effect Verification readout SI support
BIO calibration Loss of immunogenicity gate discipline PASS bits and BIO margins change SI Appendix I Tables S15-S16; SI Appendix II S.E5-S.E8
PHYS structural chemistry Loss of thermodynamic/conformational filtering DeltaG, CP, RMSD* and RMSF* sensitivity changes SI Appendix I Tables S8-S10 and S18-S20
FS/CTQW transport Loss of neighborhood-supported ranking Transport prior and entropy diagnostics change SI Appendix I Tables S9, S11 and S21-S24
MBHA boundary ledger Loss of selected/reserve margin audit Boundary state and replay hash no longer match SI Appendix I Tables S26A-S26H; SI Appendix II S.E14-S.E22

Discussion

The central result is not a claim that quantum biology has been experimentally observed in glioma neoantigen vaccination. Instead, the framework shows that quantum-state geometry and CTQW notation can be used as a disciplined mathematical language for descriptor-space transport, while non-compensatory gate logic preserves biological and chemical constraints. This is useful because peptide triage often requires many partially incompatible sources of evidence, but clinical and laboratory decisions require an explicit failure record.
The full selector improves the fixed internal benchmark while also retaining a transparent selected/reserve boundary. The distinction between selected and reserve candidates is biologically useful: reserve records can be substituted under a logged policy without reinterpreting failed candidates as acceptable. The HLA-balanced certificate also prevents one allele from dominating the panel simply because it has more high-scoring candidates. These properties are audit properties, not efficacy claims [1,11,49,50,51,52,70,71].
The most important limitation is that the current manuscript reports computational feasibility and prospective assay design, not completed experimental validation. The CD4/CD8 atlas, GL261-luc2 bridge, PET/MRI language and cytokine/T-cell readouts describe what a future authorized study should measure. They do not report survival, tumor burden, raw FCS files, cytokine measurements, animal immune response, safety or clinical outcome [78,79,80,81,82,83,84,85].

Conclusions

TAMAVAQ/Q-TAMAVAQ converts neoantigen triage into a replayable mathematical-chemistry certificate. It joins calibrated biological evidence, thermodynamic and structural descriptors, Fubini-Study-style graph geometry, CTQW support and deterministic MBHA boundary accounting while preserving non-compensatory eligibility. The fixed internal benchmark favours the full selector over graph-only and linear comparators, and the selected/reserve ledger remains inspectable. The appropriate next step is prospective laboratory validation under the assay and reporting constraints stated in the SI appendices and main text. The in vitro CD4/CD8 flow-cytometry component is positioned as graph transpost proof-of-concept validation of peptide-pool response logic.

Data Availability and Non-Clinical Study Scope

The study reports an internal Fubini-Study/CTQW-MBHA computational benchmark and an in vitro CD4/CD8 flow-cytometry proof-of-concept validation layer. The frozen replay object is defined as the candidate ledger D, calibration object C_BIO, threshold vector tau, graph G, propagation time t, score weights w, predicate oracle Phi, feasibility policy F, panel depth k, and digest H_batch. This is not a clinical trial, no patient treatment, clinical safety, clinical efficacy, survival endpoint, tumor-volume endpoint, PET/MRI response, or clinical response dataset is reported. The study is supported by the candidate ledger, code, replay manifest, supplementary appendices, and any flow-cytometry proof-of-concept data files or gating metadata in an appropriate repository, or provide a justified controlled-access statement if any data cannot be public.

Expanded Chemical and Biological Data Integration

The chemical and biological data layer is expanded here to make the final research article self-contained. The sequence-level register treats each peptide as a chemically constrained polymer with length, charge, hydrophobicity, aromaticity, anchor compatibility, contact persistence and conformational stability fields. The biological register treats presentation, processing, expression, immunogenicity and HLA compatibility as calibrated evidence sources rather than as interchangeable score columns. This separation is required because a favorable structural pose, a high expression value or a strong graph-neighborhood support term can each be useful, but none should erase a failed mandatory predicate. The SI Appendix I peptide-dashboard and structural-dashboard tables provide the detailed chemistry records; SI Appendix II provides the compact replay equations and boundary-ledger fields.
In the personalized extension, variant allele fractions and FPKM expression are used only as prior evidence. A peptide with high RNA abundance still requires allele compatibility and PASS completion, and a peptide with strong HLA binding still requires provenance, manufacturability and validation-state completeness. Table 10 links the candidate records to chemical and biological interpretation, while preserving the prospective-validation boundary stated in Figure 3 and the integrated Figure 2 atlas.
Table 10. Expanded chemical and biological evidence map. The table adds a main-text bridge from peptide chemistry and presentation biology to the non-compensatory PASS state, while keeping the prospective validation boundary explicit.
Table 10. Expanded chemical and biological evidence map. The table adds a main-text bridge from peptide chemistry and presentation biology to the non-compensatory PASS state, while keeping the prospective validation boundary explicit.
Evidence block Representative variables Chemical/biological role Mandatory gate Failure mode SI linkage
Sequence chemistry Length, MW, GRAVY, charge, anchors Defines peptide chemistry before HLA and synthesis evaluation CMC/PHYS invalid alphabet, instability, synthesis risk SI Appendix I Tables S13-S24
Presentation biology HLA, IC50 percentile, processing, TAP Defines allele-constrained presentation support BIO weak or incompatible presentation SI Appendix I Tables S41-S49; SI Appendix II S.E5-S.E12
Structural chemistry DeltaG proxy, CP, RMSD*, RMSF* Prevents single-pose overinterpretation PHYS unfavorable energy or unstable conformer SI Appendix I Tables S25-S40
Graph geometry K_ij, d_FS, W_ij, L, p_i(t) Adds neighborhood support without replacing gates GEOM isolated or incoherent evidence neighborhood SI Appendix II Tables SII4-SII6
Boundary ledger b_ir, PASS_i, S_MBHA, Gamma_i Records selected/reserve/fail state and replay margin PASS compensatory promotion blocked SI Appendix II Table SII6a
Prospective assay CD4/CD8 strata, ELISpot, cytokines, PET/MRI Defines future validation readout only VALID no observed wet-lab evidence in this manuscript SI Appendix I Tables S85-S89

Equation-to-Claim Map

The equation list on the first pages supplies the formal notation; the following map links those equations to the claims permitted in the main text. Equations E6-E12 justify graph-transport support and probability conservation, but do not imply biological quantum coherence. Equations E3-E4 and E14-E15 justify non-compensatory exclusion, but do not imply biological efficacy. Equation E16 defines replay determinism, and equations E17-E18 define patient-specific evidence import without reporting treatment or outcome. This organization keeps the mathematical proof of chemistry in the manuscript without overstating translational evidence.
Table 11. Equation-to-claim map. Each mathematical block is linked to the interpretive claim supported by the manuscript. The mapping preserves consistency with SI Appendix I and SI Appendix II by distinguishing graph-transport support, non-compensatory exclusion, replay determinism and prospective patient-specific evidence import.
Table 11. Equation-to-claim map. Each mathematical block is linked to the interpretive claim supported by the manuscript. The mapping preserves consistency with SI Appendix I and SI Appendix II by distinguishing graph-transport support, non-compensatory exclusion, replay determinism and prospective patient-specific evidence import.
Equation group Permitted claim Not permitted Numerical anchor Where used
E1-E4 Candidate eligibility is deterministic under fixed thresholds A single score proves immunogenicity BIO >= 0.70; GEOM >= 0.75 Table 1, Table 3 and Table 5
E5-E7 Dossier states and thermodynamic terms are mathematically defined Docking score is measured ΔG without calibration ΔG° = RT ln Kd Methods and PHYS gate
E8-E12 CTQW redistributes support on a symmetric graph Biological quantum coherence is observed sum_i p_i(t)=1 Figure 2 and Table 5
E13-E16 Oracle, boundary score and replay digest are inspectable Hardware quantum speedup is established H_batch digest; PASS mask Figure 1 and Table 9
E17-E20 Patient mutation/expression evidence can be imported prospectively Clinical response or animal efficacy is reported FPKM, DNA NAF, RNA NAF, HLA Table 7, Table 8 and Figure 3

Main Figure and Table Register

The study presents three main figures. Figure 1 summarizes the audit-first workflow, Figure 2 presents the integrated CD4/CD8, peptide-pool and quantum-circuit atlas, and Figure 3 presents the HLA-balanced certificate and prospective validation bridge. The remaining numerical objects are main-text tables that record equations, gate definitions, benchmarks, peptide ledgers, ablation controls, chemical/biological evidence classes and claim boundaries.
Table 12. Main figure and table register. The figure register identifies the visual datasets and their scientific function, while the tables provide the quantitative and interpretive evidence needed for the original research article.
Table 12. Main figure and table register. The figure register identifies the visual datasets and their scientific function, while the tables provide the quantitative and interpretive evidence needed for the original research article.
Object Figure label Caption topic Scientific role
Figure 1 Figure 1 Figure 1 Audit-first workflow and certificate logic
Figure 2 Figure 2 Figure 2 Integrated CD4/CD8, peptide-pool and quantum-circuit atlas
Figure 3 Figure 3 Figure 3 HLA certificate and prospective validation bridge
Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10 and Table 11 Main-text tables Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10 and Table 11 Main-text evidence tables

Limitations and Forward Validation Logic

The final research article intentionally separates four layers of evidence. First, the internal computational layer tests whether a frozen ledger and endpoint can be replayed without label leakage. Second, the chemical layer reports whether peptide sequences, structural descriptors and thermodynamic proxies remain admissible under prespecified gates. Third, the graph-transport layer adds descriptor-neighborhood support but remains subordinate to the mandatory predicates. Fourth, the prospective biological layer states what future assays should measure, without treating design diagrams as completed validation. This layered framing is essential because peptide prioritization can otherwise drift from a reproducible computational result into unsupported biological language.
For a future wet-lab study, the synthesis/QC tier should verify identity, purity, solubility and formulation stability; the HLA/pMHC tier should measure binding and presentation; the cellular tier should test peptide-specific T-cell activation, cytokines, proliferation and cytotoxicity; and the tissue/imaging tier should quantify tumor burden and immune-cell composition under authorized animal-study governance. None of these steps is claimed as completed here. The manuscript therefore remains a theoretical and computational quantum-biology account with a prospective validation plan.
The selected/reserve distinction also has an operational implication. Reserve candidates are not failures; they are positive-margin records whose inclusion is blocked by panel quota, diversity or HLA-balance policy. Failed records, by contrast, carry a negative mandatory margin or missing field and cannot be promoted by graph support. This difference preserves the clinical and manufacturing relevance of the certificate while keeping computational claims auditable.
Table 13. Claim-scope and forward-validation guardrail. The table separates computational, chemical, graph-theoretic, prospective biological and clinical layers so that each result is interpreted at the level supported by the data.
Table 13. Claim-scope and forward-validation guardrail. The table separates computational, chemical, graph-theoretic, prospective biological and clinical layers so that each result is interpreted at the level supported by the data.
Layer What is reported What is not reported Guardrail Article placement
Computational Fixed endpoint, AP/AUROC/NDCG, replay digest External generalization claim labels withheld from preprocessing Results and Table 4 and Table 5
Chemical sequence chemistry, ΔG proxy, CP, RMSD*, RMSF* measured thermodynamics unless calibrated unit-discipline and PHYS gates Methods and Table 10
Graph/quantum notation FS kernel, CTQW support, oracle mask biological quantum coherence or hardware speedup classical graph-transport interpretation Figure 2 and equations
Prospective validation assay design, future endpoints survival, PET/MRI, FCS or cytokine outcomes claim-boundary statement Figure 3 and Discussion
Clinical no treatment or response outcome reported clinical benefit, safety or efficacy separate authorized study required Data availability and claim boundary
The article uses a consistent table structure to connect evidence class, mathematical notation, SI support and permitted claim scope. The abbreviations and equation register are placed before the Results and Methods sections so that the graph-geometric and mathematical-chemistry notation can be read without interrupting the scientific argument.

Funding

The author declares that no external financial support was received for the research, authorship, and/or publication of this article.

Data availability statement

The study uses an internal candidate ledger, calibration object, threshold vector, graph object, propagation time, score weights, predicate oracle, feasibility policy, panel depth, and replay digest as the frozen computational replay object. The in vitro CD4/CD8 flow-cytometry proof-of-concept layer is documented through flow-cytometry strata, peptide-pool logic, gating metadata, controls, and replicate structure in the supplementary records. No clinical-trial dataset, patient-treatment dataset, PET/MRI endpoint, tumor-volume endpoint, survival dataset, clinical safety dataset, or clinical response dataset is reported. The executable replay implementation, configuration files, test suite and dependency declarations are available at https://github.com/GRIGORIADIS1979/TAMAVAQ-Q-TAMAVAQ-Audit-First-Reproducible-Neoantigen-Selection-Pipeline.

Ethics statement

This work is reported as a computational and in vitro proof-of-concept study. It does not describe clinical-trial enrollment, patient treatment allocation, clinical intervention, safety assessment, therapeutic-efficacy assessment, survival analysis, tumor-burden endpoint, or imaging-response endpoint. All in vitro CD4/CD8 flow-cytometry materials and data are described within the study scope as non-clinical and computational CTQW-MBHA based bioinformatics proof-of-concept validation materials.

Author contributions

Ioannis Grigoriadis: conceptualization, methodology, computational analysis, validation design, data curation, writing - original draft, writing - review and editing.

Conflict of interest

Ioannis Grigoriadis is affiliated with Biogenea Pharmaceuticals Ltd. The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest, except for the stated affiliation.

Generative AI statement

Language-editing and formatting assistance may have been used to improve clarity. No generative AI tool is reported as a source of scientific data, in vitro measurements, computational results, references, or conclusions. The author reviewed and takes responsibility for the final content.

Supplementary material

SI Appendix I and SI Appendix II accompany this article and provide the equation blocks, tables, figure-source records, replay manifest, threshold registers, and validation metadata used by the Fubini-Study/CTQW-MBHA workflow. The supporting information can be downloaded at the website of this paper posted on Preprints.org.

Acknowledgments

The author acknowledges the computational resources, data resources, and supplementary replay records used to construct the audit ledger and non-clinical validation framework.

Abbreviations

Abbrev. Definition Abbrev. Definition
AP average precision ARRIVE Animal Research: Reporting of In Vivo Experiments
BIO calibrated biological-evidence gate CADD computer-aided drug design
CD4/CD8 cluster of differentiation 4/8 T-cell strata CD4CD8CXP manuscript-defined CD4/CD8 composite prospective flow-cytometry readout
CMC chemistry, manufacturing and controls CP contact persistence
CTQW continuous-time quantum walk D degree matrix
ELISpot enzyme-linked immunospot FPKM fragments per kilobase of transcript per million mapped reads
FS Fubini-Study-style GEOM graph-geometric evidence-neighborhood gate
GRAVY grand average of hydropathy HLA human leukocyte antigen
Kd dissociation constant L graph Laplacian or peptide length, as defined locally
MBHA modified black-hole algorithm used as deterministic boundary ledger MD molecular dynamics
MHC major histocompatibility complex MRI magnetic resonance imaging
NAF neoantigen or mutation allele fraction PASS conjunction of all mandatory eligibility gates
PET positron-emission tomography PHYS structural/energetic physical-evidence gate
PROV provenance-completeness gate PSD positive semidefinite
Q-score composite graph-transport ranking score RMSD/RMSF root-mean-square deviation/fluctuation
VALID validation-state completeness gate XAI explainable artificial intelligence

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