Four Mass Harmonics predictions sealed four days before the terrain opened. Full derivational chain. Full results. Complete falsifier adjudication. This file is self-contained.
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:
MH_Monograph.md - canonical physical bedrockMH_Origin.md - genetic-code and folding-closure branch (lines 2610-2903)MH_TVP.md - topology and provenance disciplineOperational_Stance_of_UMtts.md - terrain-first process authoritySource: MH_Monograph.md, line 181
Source: MH_Monograph.md, line 156
Source: MH_Monograph.md, lines 199-201
Source: MH_Origin.md, lines 2780-2785
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.
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.
"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.
Exclude only from a specific test, not from the release ledger:
No entry is removed because it appears unfavorable to the prediction.
"The distribution of Delaunay contact-triangle equilateralness Q▵ will shift toward 1 in resolved protein cores relative to surface, mobile, or unresolved structural terrain."
The cubic source contribution is the n=3 voice of P³GG. A nonzero cubic interaction requires three equal-magnitude wavevectors whose vector sum vanishes:
Three equal vectors that sum to zero form an equilateral 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.
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.
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▵ is an analysis readout, not a new physical coefficient.
Tested across quantile thresholds Q75, Q80, Q85, Q90. All thresholds must be reported before terrain contact.
None. Clean coordinate-geometry terrain. No consensus refinement processing between physical reality and the tested quantity (Q▵ is computed directly from Cα coordinates).
"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."
The Monograph derives the icosahedron as the maximal regular three-dimensional structure composed entirely of equilateral triangular faces. The coordinate condition produces:
The resulting closure structure contains:
The genetic-code branch gives the rotational conjugacy classes: C₂, C₃, C₅, C₅². The geometric axis counts encoded by the icosahedron:
This prediction applies to compact near-spherical cages identified geometrically before metadata symmetry labels are read. The cage subset procedure:
No icosahedral label may be used to select the subset.
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.
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.
"An icosahedral metadata label is not accepted as the geometric result. The axes must be recovered from coordinates."
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.
"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."
The MFE temporal term is 1/vₓ² ψ̈ₘ. Therefore the first, second, and third base positions are not interchangeable:
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.
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.
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.
Adjacency from the same three-dimensional Delaunay relation as Derivation 1. For residue i, the first-shell signed orientation residual:
N(i) is the Delaunay-neighbor set. No distance threshold or fitted neighborhood radius is introduced.
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.
"Within synonymous-codon matched residues, lower locally cancelled codon Orientation Δ will correspond to greater structural order and lower mobility or unresolved-density probability."
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.
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.
Tested within amino-acid identity, within organism where possible, within same structure where multiple synonymous codons occur.
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.
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.
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 |
| 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 |
Target 1 of 7. Volume I. First terrain contact of the Mass Harmonics Volume I Prediction Set.
Signal quality is distinct from verdict. The following notes describe the measurement-layer conditions that may attenuate signal. They do not alter falsifier outcomes.
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.
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.
Source: Prediction document Section XI (verbatim).
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)
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.
MH_Monograph.md - lines 130-183, 184-228, and 262-332MH_Origin.md - lines 2610-2903, especially 2641-2678, 2702-2759, and 2761-2890MH_TVP.md - complete current standalone protocolOperational_Stance_of_UMtts.md - complete operational authorityWorldwide Protein Data Bank, weekly archive update policy. Weekly advance sequences Saturday 03:00 UTC; coordinates Wednesday 00:00 UTC.
Zenodo DOI: 10.5281/zenodo.21304301
TRUTH > COMFORT. Always.
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