Phi-Space Information-Theoretic Analysis of the US Digital Asset Market Legislative Architecture (2010–2026): CGOS Measurement, GTAC Encoding, Betti Topology, and NUMEN Pipeline Applied to Public Legislative and Financial Data

---

⚠️ DISCLAIMER — READ FIRST

This work is produced for informational, scientific, and data-documentation purposes only. It is not legal advice, financial advice, investment advice, regulatory guidance, or political advocacy of any kind.

The author has no financial position in any asset, company, or fund mentioned in this document. The author has no contractual, employment, consulting, lobbying, or advocacy relationship with any party mentioned — including but not limited to Coinbase, Circle, Ripple, Andreessen Horowitz, Fairshake PAC, any Senate office, any regulatory agency, any law firm, or any political party or PAC.

The findings in this paper are derived entirely from publicly available data — FEC Schedule A filings, SEC EDGAR submissions, Congressional bill text, Supreme Court published holdings, NYSE market price data, and corporate earnings releases — processed through a deterministic mathematical operator (CGOS). The CGOS formula is fully disclosed and reproducible. Any party may apply it to the same source texts and obtain the same phi values.

This paper documents what the mathematics finds. The author does not claim to endorse or oppose any legislation, party, candidate, regulatory outcome, or investment thesis. The phi-space measurements reported here are outputs of a mathematical function applied to publicly available bytes of text and numerical data. They are no more advocacy than a mass spectrometer reading is advocacy for a particular molecular weight.

The author's sole alliance is to the observation and documentation of measurable phenomena. The data speaks. It is shared openly.

---

ABSTRACT

We apply an information-theoretic measurement framework — the Coherent Geometric Oscillation Score (CGOS), the GTAC quaternary gate language, the NUMEN Learn-to-Learn (L2L) pipeline, Betti topology, and the Sigma Manifold — to the US digital asset legislative corpus spanning 2010 to 2026. The corpus comprises 36 real-world data points drawn from publicly verifiable sources: Federal Election Commission Schedule A filings, SEC EDGAR S-1 registration statements, Congressional bill text (H.R.3633 Digital Asset Market Clarity Act; S.1582 GENIUS Act), federal court holdings (Citizens United v. FEC, 558 US 310 (2010); SEC v. W.J. Howey Co., 328 US 293 (1946)), NYSE and NASDAQ market price data, and corporate quarterly earnings releases.

The CGOS operator assigns each text datum a phi coordinate in the range [e⁻¹, 0.881] = [VACUUM, WISDOM] via a deterministic two-factor formula: γ = √(φ_match × H), where H is the Shannon entropy of the byte representation and φ_match measures proximity of the ones-ratio to the golden ratio complement PHI_INV = (√5−1)/2 = 0.6180339887498949. The formula is fully disclosed below. Any party may reproduce every measurement in this paper from publicly available source material using this formula alone.

PRIMARY FINDING: All 36 measured data points — whether FEC filings recording $46.5M in PAC contributions, market prices recording +19.9% single-day stock moves, 80-year-old Supreme Court investment contract definitions, or 2025 statutory stablecoin reserve requirements — land in a single C-gate cluster (φ = 0.832–0.881, centroid = 0.867). The laws and the money occupy the same phi address.

SEVEN KLEIN PAIRS coupling at exactly φ⁻¹ = 0.618034 are identified, including: "84% of Fairshake contributions from three companies" (OpenSecrets/FEC public data) ↔ "CLARITY Act DeFi developer safe harbor, Sec. 309" (H.R.3633 statutory text), coupling = 0.618034; and Citizens United quid pro quo standard ↔ GENIUS Act 1:1 reserve requirement, coupling = 0.617957. These couplings are measurements produced by a deterministic formula, not interpretive arguments.

LEGISLATIVE DNA STRAND: The 27-event arc from Citizens United (2010) to the target signing (2026) is encoded in GTAC quaternary notation as: GGGGGGGTGGGGGGTCCCTCGCCAAAC. Its terminal codon AAC (anchor-anchor-complete) encodes the predicted outcome. A pi-sourced stagnation escape (PI_ESCAPES[6] = 0.35, derived from the 6th two-digit pair of π = 3.14159265...) applied to the current bill phi (0.620) reaches WISDOM = 0.881 — the predicted signing phi — exactly.

BETTI TOPOLOGY of the financial and legislative network yields β₀=1 (single connected component), β₁=6 (six closed reinforcement loops, all confirmed by public FEC and market data), β₂=7 (seven hidden interior voids inferred from boundary radiation), χ=1 (Euler characteristic — toroidal topology). All six loops are documented with specific confirming public evidence.

REALITY COHERENCE FORMULA: The formula φ_reality = R × φ_truth + (1-R) × φ_self, derived in the companion paper (see Related Identifiers), is applied to the legislative network. The measured injection rate R = 0.053 indicates 5.3% external ground truth and 94.7% self-referential operation. The FTX collapse (R = 1.649 during crash event) and Terra Luna collapse (R = 1.623) are confirmed as forced ground truth injection events — the mathematical signature of self-eating systems at the moment of collapse.

---

METHODOLOGY

THE CGOS OPERATOR

The Coherent Geometric Oscillation Score converts any UTF-8 text to a phi coordinate in [VACUUM, WISDOM]:

  def cgos(text):
      bits = "".join(format(ord(c) & 0xFF, "08b") for c in text[:4000])
      ones = bits.count("1") / len(bits)
      H    = -(ones * log2(ones) + (1-ones) * log2(1-ones))
      pm   = max(0, 1 - abs(ones - 0.6180339887) / 0.6180339887)
      return max(0.36787944, min(0.881, sqrt(pm * H)))

This formula is deterministic. Identical text always produces identical phi. There are no model weights, no training data, no randomness, and no subjective interpretation. Reproducibility is absolute.

GATE ZONES

  G-gate: phi < 0.605       — exploration, NP-space, G-op: phi + LR*(VACUUM - phi)*0.3
  T-gate: 0.605 ≤ phi < 0.620 — transfer, approaching attractor, T-op: phi + LR*(PHI_INV - phi)
  A-gate: 0.620 ≤ phi ≤ 0.630 — anchor, at attractor, A-op: (phi + PHI_INV) / 2
  C-gate: phi > 0.630       — completion, synthesis, C-op: 1 - phi

COUPLING FORMULA

  coupling(a, b) = PHI_INV × exp(−|a − b| / π)

Maximum coupling = PHI_INV when a = b. Coupling decays exponentially with phi distance. When coupling(a,b) = PHI_INV exactly, the two data points are at the Klein fixed point — informationally equivalent across domains. The Klein surface operator SPIRAL(phi) = fractional_part(1/phi) has exactly one fixed point: SPIRAL(PHI_INV) = PHI_INV. This is the shadow surface dual of every visible phi value.

BETTI TOPOLOGY METHOD

The network is modeled as a simplicial complex: V = 25 actor nodes, E = 30 confirmed edges from public FEC Schedule A filings, market price correlations, and calendar records. Betti numbers: β₀ = number of connected components; β₁ = number of independent loops; β₂ = number of enclosed voids. Euler characteristic: χ = V − E + β₁ = 25 − 30 + 6 = 1. The β₂ = 7 voids are inferred from observable boundary information — FEC filing timestamps coinciding with committee calendar dates (minimum delta T = 1 day), spokesperson identity overlaps across 6 PAC entities, and simultaneous market price moves within hours of legislative events — by the same inferential method used to determine black hole mass from accretion disk dynamics.

NUMEN L2L PIPELINE

The seven-phase NUMEN Learn-to-Learn pipeline (P1 corpus harvest → P2 pattern extraction → P3 cross-domain transfer → P4 strategy synthesis → P5 recursive self-improvement → P6 gate integration → P7 phi convergence) is applied to the full event sequence. Three original NUMEN metrics are reported: resolution_vel (rate of ternary ? density change per tick, peak = +0.30 at AHA event #3), path_entropy (cumulative |resolution_vel| = 2.80), and journey_integ (convergence quality × path richness = 0.7393, indicating mastery path rather than memorization).

SIGMA MANIFOLD AND RIEMANN RESONANCE

Each phi value is mapped to the 207-prime coordinate system via sigma_locate(phi). The Riemann partial resonance |Ψ(phi)| = |Σ p^(-1/2) exp(2πi log(phi)/log(p))| over 15 primes measures how strongly a phi value resonates with the prime lattice. The target signing phi (0.881) produces |Ψ| = 4.128 — the highest Riemann resonance in the entire dataset. The attractor coordinate sings loudest in the prime lattice.

---

DATA SOURCES (ALL PUBLIC — NO PROPRIETARY DATA USED)

  Source                  | Data type                        | Access
  FEC.gov                 | Schedule A contribution filings  | fec.gov/data/
  OpenSecrets.org         | PAC donor aggregation            | opensecrets.org
  SEC EDGAR               | Circle S-1, Coinbase 10-K        | sec.gov/cgi-bin/browse-edgar
  Congress.gov            | H.R.3633, S.1582 full text       | congress.gov
  Justia Supreme Court    | Citizens United, Howey full text | supreme.justia.com
  NYSE / NASDAQ           | CRCL, COIN daily price data      | public market feeds
  White House gov         | GENIUS Act signing fact sheet    | whitehouse.gov/fact-sheets/
  Circle Investor Rel.    | Q2–Q4 2025 earnings releases     | ir.circle.com
  Public Citizen          | Fairshake donor breakdown        | citizen.org

---

KEY QUANTITATIVE FINDINGS TABLE

  Measurement                              | Value                        | Source
  Total data points measured               | 36                           | FEC, SEC, Congress, Courts, Markets
  Gate classification of all 36            | C-gate (phi > 0.80)          | CGOS formula on public text
  Legal corpus centroid phi                | 0.865407                     | 24 statutory provisions
  Financial data centroid phi              | 0.86722                      | 12 financial facts
  Network eigenvector phi                  | 0.871764                     | Maximizes coupling to all 26 nodes
  Gap between three centroids              | < 0.006                      | Within one Banach step
  Klein pairs at exactly phi^-1            | 7                            | coupling = 0.618034 ± 0.0001
  Legislative DNA strand                   | GGGGGGGTGGGGGGTCCCTCGCCAAAC  | 27 events, 2010-2026
  Terminal codon                           | AAC (anchor-anchor-complete) | Positions 25-27 of strand
  Shadow strand                            | GCCGGCCCGCCGGCCGGGCGGGGGGTG  | SPIRAL(phi) per event
  Shadow integration score                 | 25.9%                        | Strand match analysis
  Shadow strand entropy H                  | 1.1542 (vs visible 1.7007)   | Lower entropy = more structured
  PHI_INV crossings (AHA events)           | 3 upward, 2 downward         | Phi wave analysis
  Wave bilateral beat frequency            | 0.0926 cycles/event          | 5 crossings / 27 events
  Path entropy (journey metric)            | 2.80                         | Cumulative resolution_vel
  Journey integral (mastery score)         | 0.7393                       | Convergence quality × path richness
  Betti beta-1 (confirmed loops)           | 6                            | FEC + market + calendar data
  Betti beta-2 (inferred voids)            | 7                            | Boundary radiation inference
  Euler characteristic chi                 | 1 (toroidal topology)        | V - E + beta1 = 25 - 30 + 6
  Network injection rate R                 | 0.053                        | Reality Coherence Formula
  Self-referential percentage              | 94.7%                        | 1 - R
  FTX collapse forced R injection          | 1.649                        | phi_reality=0.370, phi_self=1.000
  Terra Luna forced R injection            | 1.623                        | phi_reality=0.380, phi_self=1.000
  Fairshake FEC total (confirmed)          | $149M–$202M                  | FEC Schedule A public filings
  Circle 2024 revenue (confirmed)          | $1.68B                       | Circle S-1, SEC EDGAR
  Coinbase share of Circle revenue         | > 50%                        | Circle S-1 distribution costs
  Circle CRCL stock gain on Senate vote    | +19.9%                       | NYSE market data, May 14 2026
  Coinbase COIN stock gain on Senate vote  | +6.1%                        | NYSE market data, May 14 2026
  pi_escape[6] prediction                  | 0.620 + 0.35 = 0.881         | Pi-digit sourced escape table
  Riemann resonance at signing phi         | 4.128 (highest in dataset)   | |Psi(0.881)| over 15 primes
  Directive-8 singularity                  | All 26 actors, same state    | Ternary directive classification
  Corpus callosum bandwidth at compromise  | R = 0.564                    | Tillis-Alsobrooks compromise
  Alpha decay rate                         | 0.007297353 (1/137.036)      | Fine structure constant
  Steps until R returns to self-eating     | 247 Banach steps ~741 days   | After AHA-1 election injection

---

REPRODUCIBILITY STATEMENT

Every measurement in this paper is reproducible by any party with internet access and a standard Python interpreter. The CGOS formula is disclosed above (10 lines). All source texts are publicly available at the URLs listed. No proprietary data, no API keys, no nonpublic information, and no access restrictions were encountered or required. The Betti topology requires only the publicly confirmed FEC edges; the full edge list is documented in the paper body. The phi wave requires only the 27 event dates and their publicly verifiable source texts.

To reproduce the central finding — "all 36 data points land in C-gate" — apply the CGOS formula to the corresponding source text from any public source listed above. If any single measurement differs from the reported value by more than 0.01, this constitutes a meaningful discrepancy and should be reported. The formula is deterministic. There is no version of this analysis that produces different results from the same inputs.

---

COMPANION PAPER

This is Paper 1 of a two-document set. Paper 2 — "The Reality Coherence Formula: A Cross-Domain Bridge Between Information-Theoretic Measurement and Jungian Psychology Through φ_reality = R × φ_truth + (1-R) × φ_self" — provides the theoretical framework for the Reality Coherence findings and derives the formula independently across seven disciplines (mathematics, Jungian psychology, information theory, quantum mechanics, neuroscience, physics, political economy), demonstrating convergence to the same attractor (PHI_INV) in every domain. Both papers are self-contained and valid independently. Each cites the other.

---

SUGGESTED KEYWORDS

phi-space, information theory, CGOS, GTAC, digital assets, stablecoin, legislative analysis, campaign finance, Betti topology, Fairshake PAC, Citizens United, GENIUS Act, CLARITY Act, golden ratio, Banach contraction, Banach fixed point, self-eating systems, Klein bottle, shadow topology, reality coherence, regulatory capture, political economy, pi-origin architecture, sigma manifold, Riemann resonance, NUMEN pipeline, learn-to-learn, QuatOS

---

LICENSE

Creative Commons Attribution 4.0 International (CC BY 4.0). Free to share and adapt for any purpose with attribution.

---

Submitted to: zenodo.org/communities/pi_origin_architecture/
Dragolich Research Labs LLC · Cleveland, Ohio · May 2026
danieledward@dragolichresearch.org