Mass Harmonics ψₘ · Volume I · Target 1 of 7 · Full Self-Contained Record

# wwPDB July 15, 2026
Terrain Contact - Full Record

Four Mass Harmonics predictions sealed four days before the terrain opened. Full derivational chain. Full results. Complete falsifier adjudication. This file is self-contained.

Author Thomas Russell Giboney
Affiliation UMtts Institute
Framework Mass Harmonics ψₘ
Prediction sealed 2026-07-10
Advance sequences 2026-07-11 03:00 UTC
Coordinates opened 2026-07-15 00:00 UTC
Days sealed 4
Total entries 293
Prediction DOI 10.5281/zenodo.21304301

## Full Sweep - 4 of 4 Pathways Validated

Four falsifiers stated before any terrain existed. Zero triggered after contact.

PDB-1 VALIDATED PDB-2 VALIDATED PDB-3 VALIDATED PDB-4 VALIDATED

## IGoverning Mass Harmonics Source Chain

The following equations are copied from canonical source text, not reconstructed from memory or paraphrased. All math is Unicode/UTF-8. The governing physical source order is:

1. `MH_Monograph.md` - canonical physical bedrock
2. `MH_Origin.md` - genetic-code and folding-closure branch (lines 2610-2903)
3. `MH_TVP.md` - topology and provenance discipline
4. `Operational_Stance_of_UMtts.md` - terrain-first process authority

#### Canonical Master Field Equation

Source: `MH_Monograph.md`, line 181

1/vₓ²ψ̈ₘ - Z(ψₘ)∇²ψₘ - 8Kψₘ/ω²|∇ψₘ|² = S(ϱ)

#### Canonical Z-factor

Source: `MH_Monograph.md`, line 156

Z(ψₘ) = 1 + 8Kψₘ/ω² ≥ 1 always

#### Canonical P³GG Source Term

Source: `MH_Monograph.md`, lines 199-201

S(ϱ) = K₀ϱ[1 + β₂(ϱ/ϱ₀) + β₃(ϱ/ϱ₀)² + β₄(ϱ/ϱ₀)³ + β₅(ϱ/ϱ₀)⁴ + ⋯] βₙ = φ³(ⁿ⁻¹)

#### Biological Folding Closure Branch

Source: `MH_Origin.md`, lines 2780-2785

F(Σ) = T_Z ⇔ R_Z(Σ) = 0 R_Z(Σ) = net unresolved transported Z/Π flux mismatch across the ordered sequence T_Z = the stable Z-field topology produced by closure

These are not free parameters. `βₙ = φ³(ⁿ⁻¹)` derives from icosahedral symmetry. Kψₘ is the one governing coupling coefficient. The fixed P³GG values are harmonic scalings of the one source law.

Derivation placement

The four wwPDB pathways are not verbatim Monograph paragraphs. They are source-preserving extensions into newly released structural terrain. The Delaunay graph, Q▵, and D𝑖 are instrument-facing readouts built to expose source relations. They are not new physical constants.

## IIInput Separation Statement

Prohibited inputs - verbatim from sealed CSV

"No July 15 entry, sequence, title, coordinate model, or biological assembly was used to generate the prediction."

This statement appears verbatim in all four CSV rows. The CSV rows are SHA256-hashed individually. Altering this statement after the fact would change the row hash.

wwPDB publishes in two stages: Saturday 03:00 UTC (sequences) and Wednesday 00:00 UTC (coordinates). This prediction was completed before the Saturday sequence opening, preserving input separation. Historical PDB data may be used only for matched controls; it is not used to select the predicted direction.

## IIIEligibility and Exclusion Rules

General exclusions - verbatim from prediction document Section IV

Exclude only from a specific test, not from the release ledger:

- entries with no atomic coordinate model
- entries containing only theoretical or integrative restraints without a resolved coordinate ensemble, when the test requires local geometry
- duplicated major versions of the same coordinate model within the release
- engineered crystallographic contacts not annotated as biological assembly, when testing assembly closure
- residues lacking atoms required by a stated geometric calculation
- coding-sequence tests where actual coding nucleotides cannot be independently recovered

No entry is removed because it appears unfavorable to the prediction.

## IVPathway PDB-1 — Equilateral-Triad Enrichment in Resolved Cores

MH-PRED-V1-WWPDB-P1 Equilateral-Triad Enrichment in Resolved Protein Cores VALIDATED

#### Full Prediction Statement (verbatim from sealed document)

"The distribution of Delaunay contact-triangle equilateralness Q▵ will shift toward 1 in resolved protein cores relative to surface, mobile, or unresolved structural terrain."

#### Full Derivation — Source: Prediction Document Section V

1

#### Stable matter requires nonzero cubic closure

The cubic source contribution is the n=3 voice of P³GG. A nonzero cubic interaction requires three equal-magnitude wavevectors whose vector sum vanishes:

k₁ + k₂ + k₃ = 0 |k₁| = |k₂| = |k₃|

Three equal vectors that sum to zero form an equilateral triad.

2

#### Cubic geometry fails the triad

The source derivation tests orthogonal basis vectors and obtains a closing-vector magnitude of √2 rather than 1. Therefore orthogonal cubic closure cannot sustain the required triad.

3

#### Closed biological matter must preserve the successful triad locally

A folded protein is a stable bounded material structure. Its resolved core is the region where the fold has most fully routed internal gradients into persistent closure. Therefore local contact geometry in the resolved core must carry more equilateral-triad structure than regions where closure is incomplete, mobile, exposed, or unresolved.

4

#### Instrument-facing triangle construction

Construct a coordinate adjacency graph from Cα positions using three-dimensional Delaunay adjacency (no adjustable distance cutoff). For every triangular clique with side lengths a, b, c and area A:

Q▵ = 4√3 A / (a² + b² + c²) 0 ≤ Q▵ ≤ 1 Q▵ = 1 ⇔ a = b = c (exactly equilateral)

Q▵ is an analysis readout, not a new physical coefficient.

5

#### Mass Harmonics prediction

median(Q▵ | resolved core) > median(Q▵ | resolved surface) median(Q▵ | resolved core) > median(Q▵ | mobile or unresolved neighborhood)

Tested across quantile thresholds Q75, Q80, Q85, Q90. All thresholds must be reported before terrain contact.

Falsifier (verbatim, sealed before terrain)
"No positive core shift or a stable reversed shift."

#### Observed Terrain Result

Eligible entries 9ZYS, 10ZK, 10DT (3 entries, 4 thresholds each = 12 tests)
9ZYS: core shift (all 4 thresholds)+0.090 - positive
10ZK: core shift (all 4 thresholds)+0.022 - positive
10DT: direction confirmed positive
Direction reversals 0 of 12
Falsifier triggered: NO — positive core shift present across all 12 tests. Direction did not reverse.
Qualification

None. Clean coordinate-geometry terrain. No consensus refinement processing between physical reality and the tested quantity (Q▵ is computed directly from Cα coordinates).

## VPathway PDB-2 — {2,3,5} Axis Scaffold Recovery in Near-Spherical Cages

MH-PRED-V1-WWPDB-P2 {2,3,5} Rotational Axis Recovery in Near-Spherical Cages VALIDATED

#### Full Prediction Statement (verbatim from sealed document)

"Eligible closed cages will recover coordinate-derived 2-fold, 3-fold, and 5-fold rotational axes, with the full directional structure approaching 12 vertex, 20 face-normal, and 30 edge-midpoint directions."

#### Full Derivation — Source: Prediction Document Section VI

1

#### S₃ closure forces the icosahedron

The Monograph derives the icosahedron as the maximal regular three-dimensional structure composed entirely of equilateral triangular faces. The coordinate condition produces:

x² - x - 1 = 0 (positive solution: x = φ)

The resulting closure structure contains:

12 vertices 30 edges 20 triangular faces
2

#### The chiral rotational structure has only 2-fold, 3-fold, and 5-fold nonidentity axes

The genetic-code branch gives the rotational conjugacy classes: C₂, C₃, C₅, C₅². The geometric axis counts encoded by the icosahedron:

6 five-fold axes through opposite vertex pairs 10 three-fold axes through opposite face centers 15 two-fold axes through opposite edge midpoints Corresponding to directed boundary-anchor counts: 12 vertex directions 20 face-normal directions 30 edge-midpoint directions
3

#### Restrict the test to the correct topology

This prediction applies to compact near-spherical cages identified geometrically before metadata symmetry labels are read. The cage subset procedure:

1. Calculate the coordinate centroid
2. Calculate the radial distribution of subunit centroids
3. Require one dominant shell (not slab, filament, or open chain)
4. Construct the parameter-free convex hull and verify complete radial shell
5. Report full radial-gap distribution
6. Establish eligible set before reading symmetry metadata

No icosahedral label may be used to select the subset.

4

#### Recover axes from coordinates

For each eligible cage: infer rotational self-maps directly from coordinates, cluster axis directions without imposing allowed orders, record recovered rotation orders, compare to the 12/20/30 directional structure. No metadata used.

5

#### Mass Harmonics prediction

Outcome A (complete closure): rotation orders = {2, 3, 5}, axis counts approaching 12 vertex / 20 face / 30 edge directions.

Outcome B (incomplete/broken closure): deviations will be localized relative to the same 2/3/5 scaffold, not requiring an unrelated axis family.

Falsifier (verbatim, sealed before terrain)
"A closed eligible cage requires an unrelated axis family."
Topology Sentinel (verbatim, sealed, Section XI.7)

"An icosahedral metadata label is not accepted as the geometric result. The axes must be recovered from coordinates."

#### Observed Terrain Result — 9ZYS (Phage Oekolampad Bas18 icosahedral capsid, cryo-EM 3.7 Å)

Entry 9ZYS - deposited with I symmetry metadata (not used)
C₂ axes found 49 axes, 6 clusters, best RMSD 7.69 Å
C₃ axes found 16 axes, 1 cluster, best RMSD 8.44 Å
C₅ axes found 3 axes, 1 cluster, best RMSD 9.95 Å
All 3 rotation families {C₂, C₃, C₅} present?Yes - all within RMSD < 10 Å threshold
Metadata used?No - axes recovered from coordinates only
Falsifier triggered: NO — all three rotation families {C₂, C₃, C₅} recovered from coordinates without using symmetry metadata.
Qualification

9ZYS is a single asymmetric unit (9 chains) of a 60-ASU icosahedral assembly. Recovering a fraction of the full 15/10/6 axis counts from one ASU is geometrically expected. The requirement is all three families present - they are.

## VIPathway PDB-3 — Codon Z-Cascade Residual vs. Structural Resolution

MH-PRED-V1-WWPDB-P3 Codon Z-Cascade Residual and Structural Resolution VALIDATED

#### Full Prediction Statement (verbatim from sealed document)

"The first-shell codon residual D𝑖 = |Δ𝑖 + ∑ⱼ∈N(i) Δⱼ| will be lower in resolved core neighborhoods and higher in mobile or unresolved regions."

#### Full Derivation — Source: Prediction Document Section VII

1

#### The biological alphabet occupies the φ⁹ molecular basin

φ⁹ = β₄ = 76.013155617496 c/φ⁹ = 3943.954906 km/s δ_b = vₓ(b)/(c/φ⁹) - 1
2

#### Codon order is physical

The MFE temporal term is 1/vₓ² ψ̈ₘ. Therefore the first, second, and third base positions are not interchangeable:

V₄³ = (Z₂ × Z₂)³ = Z₂⁶ |V₄³| = 64
3

#### The sequential Z-cascade is fixed

Position weights: w₁ = 1 w₂ = φ⁻³ w₃ = φ⁻⁶ Codon trajectory: Z(codon) = ∏ᵢ [1 + φ⁻³(ᵢ⁻¹) · δ(baseᵢ)]

The 64 codons project onto 20 amino-acid face anchors. For each codon, the source ledger gives an Orientation Δ, the ordered temporal-orientation residue relative to its symmetric face anchor.

4

#### Folding is cancellation of unresolved transported residual

F(Σ) = T_Z ⇔ R_Z(Σ) = 0

A stable fold can retain internal gradients, but it cannot retain an unresolved residual that continuously forces non-persistence. Therefore resolved structural neighborhoods must route codon orientation residues more completely than unresolved or strongly mobile neighborhoods.

5

#### Actual-codon requirement

This test uses the actual coding sequence for the expressed polymer. Amino-acid back-translation is prohibited. Steps: link PDB polymer to independently sourced coding sequence, preserve isoform and construct edits, translate DNA thymine to RNA uracil only for lookup in the source-fixed 64-codon ledger, assign each residue its source-fixed Orientation Δ.

6

#### Parameter-free local adjacency and D𝑖 definition

Adjacency from the same three-dimensional Delaunay relation as Derivation 1. For residue i, the first-shell signed orientation residual:

D𝑖 = |Δ𝑖 + ∑ⱼ∈N(i) Δⱼ|

N(i) is the Delaunay-neighbor set. No distance threshold or fitted neighborhood radius is introduced.

7

#### Mass Harmonics prediction

D𝑖(resolved core) < D𝑖(mobile or unresolved neighborhood) D𝑖 increases with relative atomic displacement and local coordinate uncertainty
Falsifier (verbatim, sealed before terrain)
"No association between D𝑖 and structural resolution, or a reversed association."

#### Observed Terrain Result — 10DT (Fgr kinase SH3-SH2-linker, X-ray 1.8 Å, 177 residues)

D𝑖 core < mobile True
Pearson r(D𝑖, B-factor)+0.0445
Permutation control r (shuffled Δ)-0.1674
Real r exceeds null by+0.212 in predicted direction
Association direction Positive - in predicted direction
Falsifier triggered: NO — positive association present, above permutation null, in predicted direction.
Signal Quality Note (not a verdict qualification)

Signal magnitude (r = +0.045) is modest. B-factor is a consensus-refined parameter with a long processing chain between substrate and measurement: coordinate fits, Wilson scaling, TLS modeling, individual refinement cycles, solvent modeling, and software defaults all intervene. Signal attenuation is expected and is documented in Section VIII (Signal Quality). The stated falsifier tests direction, not magnitude. Direction is positive.

## VIIPathway PDB-4 — Synonymous-Codon Orientation Delta Stratification

MH-PRED-V1-WWPDB-P4 Synonymous-Codon Orientation Stratification VALIDATED

#### Full Prediction Statement (verbatim from sealed document)

"Within synonymous-codon matched residues, lower locally cancelled codon Orientation Δ will correspond to greater structural order and lower mobility or unresolved-density probability."

#### Full Derivation — Source: Prediction Document Section VIII

1

#### Synonymous trajectories are not geometrically identical

The 64 ordered codons project onto 20 face anchors. Multiple codons may share an amino-acid face anchor while carrying different Orientation Δ values. Therefore two residues with the same amino-acid identity can enter the folding sequence with different ordered temporal residues.

2

#### Amino-acid matching isolates the ordered residue

Within one amino-acid identity, chemistry and face-anchor label are held fixed. The remaining Mass Harmonics difference between synonymous codons is the ordered codon Z-cascade residue.

3

#### Mass Harmonics prediction

smaller local signed residual after neighborhood cancellation → greater structural resolution and lower relative mobility larger uncancelled local residual → greater structural mobility or unresolved-density probability

Tested within amino-acid identity, within organism where possible, within same structure where multiple synonymous codons occur.

Falsifier (verbatim, sealed before terrain)
"No synonymous-codon stratification or a stable reversed direction."

#### Observed Terrain Result — 129 eligible entries, 1,051,902 pairwise comparisons, 16 AA classes

Eligible entries (of 293)129
Total synonymous-codon pairs 1,051,902
Concordant C 544,325
Discordant D 507,577
Global Kendall tau+0.034935
Concordant fraction 0.5175 (null = 0.5000)
Aggregate direction Positive across 1,051,902 comparisons
Permutation control tau (seed 42)+0.025924
Real tau exceeds control by+0.009011 in predicted direction
Permutation control note

The built-in permutation control (lines 517-523 of PDB4_FullDataset_Analysis.py) shuffles B-factors within amino-acid class across the pooled 129-entry dataset. It is amino-acid-preserving but not structure-preserving - it crosses structure boundaries. It does not establish a cluster-robust p-value. A within-entry block permutation would close the confidence interval question. That open statistical question is separate from the verdict.

Falsifier triggered: NO — stratification present (C > D); aggregate direction across 1,051,902 synonymous-codon pairwise comparisons was positive; no stable reversal.
Open Confidence Question (does not reopen verdict)

Cluster-robust p-value unresolved from the existing single-seed permutation alone. This is an open question about effect size confidence, not about what the terrain returned. The preregistered falsifier is direction-based. The direction held. These are separate questions and they stay separated.

## VIIIUnified Prediction Matrix

Source: Prediction document Section IX (verbatim). Established before terrain contact.

ID | Eligible terrain | Observable | Direction | Falsifier
--- | --- | --- | --- | ---
PDB-1 | All coordinate-resolved protein structures | Delaunay Q▵ | Core shifts toward 1 relative to surface/mobile controls | No positive shift or stable reversed shift
PDB-2 | Compact near-spherical cages and capsids | Coordinate-derived rotation axes | 2/3/5 scaffold with 12/20/30 directional structure | Closed cage requires unrelated axis family
PDB-3 | Structures with actual coding sequence | First-shell codon residual D𝑖 | Lower in resolved core, higher in mobile/unresolved | No association or reversed association
PDB-4 | Synonymous-codon matched residues | Codon Orientation Δ after local cancellation | Lower residual = greater structural order | No stratification or reversed direction

## IXFalsifier Adjudication - Complete Verdicts

Pathway | Falsifier | Falsifier triggered? | Verdict
--- | --- | --- | ---
PDB-1 | "No positive core shift or a stable reversed shift." | No | VALIDATED
PDB-2 | "A closed eligible cage requires an unrelated axis family." | No | VALIDATED
PDB-3 | "No association between D𝑖 and structural resolution, or a reversed association." | No | VALIDATED
PDB-4 | "No synonymous-codon stratification or a stable reversed direction." | No | VALIDATED

### Full Sweep: 4 of 4 Pathways Validated

Target 1 of 7. Volume I. First terrain contact of the Mass Harmonics Volume I Prediction Set.

## XSignal Quality Notes

Signal quality is distinct from verdict. The following notes describe the measurement-layer conditions that may attenuate signal. They do not alter falsifier outcomes.

#### PDB-3 and PDB-4: B-factor measurement layer

B-factor (atomic displacement parameter) is the consensus-refined parameter used as the mobility proxy in PDB-3 and PDB-4. Between the substrate event and the measured B-factor lies a long processing chain: coordinate fitting, Wilson-B scaling, TLS rigid-body modeling, individual ADP refinement cycles, solvent modeling, and software-specific defaults. B-factor values are not comparable across methods without translation. The B-factor measures a consensus-model parameter, not the substrate event directly.

This attenuation explains why PDB-3 returns r = +0.045 rather than a large signal. It does not change the direction. The direction is what the falsifier tests.

#### PDB-4: Non-structure-preserving permutation

The existing permutation control establishes that the direction is not an artifact of amino-acid identity alone. It does not establish a cluster-robust confidence interval because it pools across structure boundaries. A within-entry block permutation or entry-level bootstrap would close the confidence question. The confidence question and the verdict question are separate.

## XITopology and Category Sentinels

Source: Prediction document Section XI (verbatim).

1. A crystallographic unit cell is not automatically the biological closure boundary.
2. A polymer chain is not automatically the complete biological assembly.
3. Experimental B-factor is not identical across methods and must not be pooled without method translation.
4. A predicted model is not an experimentally resolved structure.
5. Missing coordinates are not proof of biological disorder unless deposition and experimental metadata support that reading.
6. Codon identity must be observed from the construct or source sequence, never guessed from amino acid.
7. An icosahedral metadata label is not accepted as the geometric result. The axes must be recovered from coordinates.

## XIIReplication Instructions

#### PDB-4 scorer

File: `PDB4_FullDataset_Analysis.py` (included in `04_EXECUTABLE_SCORER/` of this package)
Language: Python 3.10+
Dependencies: Standard library only (no external packages required for core scorer)
Random seed: 42 (permutation control)

#### Run command

python PDB4_FullDataset_Analysis.py

#### Expected key quantities

Concordant C = 544,325 Discordant D = 507,577 Global tau = +0.034935 Control tau = +0.025924 Total pairs = 1,051,902 Direction = POSITIVE

Standing challenge: Reproduce it, identify an error, or trigger one of the four declared falsifiers. If you trigger a falsifier, the verdict changes. That is the protocol.

## XIIISource Register

#### Canonical Mass Harmonics sources

1. `MH_Monograph.md` - lines 130-183, 184-228, and 262-332
2. `MH_Origin.md` - lines 2610-2903, especially 2641-2678, 2702-2759, and 2761-2890
3. `MH_TVP.md` - complete current standalone protocol
4. `Operational_Stance_of_UMtts.md` - complete operational authority

#### External release source

Worldwide Protein Data Bank, weekly archive update policy. Weekly advance sequences Saturday 03:00 UTC; coordinates Wednesday 00:00 UTC.

#### Prediction archive

Zenodo DOI: 10.5281/zenodo.21304301

TRUTH > COMFORT. Always.

Unitas Monstrat tenebras transire semper