Complementary triplet split of 142857. Digits at positions i and i+3 sum to 9: pairs {1,8}, {4,5}, {2,7}.
Raw STOR = k × 10⁻⁶ counts every Hard Stop as +1. Weighted STOR = Σ wᵢ × 10⁻⁶ instead deposits the intent weight of each stop (−1…+3). The raw line is just the special case where every stop is +1 (self-resolution). Under Information-Centric Gravitation the net weight W = Σ wᵢ is the loop's mass contribution — negative-weight (hate) stops remove field weight; love/mercy stops add more than one. Explore this fully in the Intent Weight tab.
Minimum 2 complete cycles (12) + 1 entry = 13 positions to verify a period-6 signal.
CLICK ANY NODE TO EXPLORE
The Intent Topology maps moral and emotional states onto the six full rotations of the loop — n/7 for n = 1…6 (0.142857 through 0.857142). Each rotation is a distinct fractional state that has not yet reached resolution; the framework treats intention as what determines whether, and how, a loop reaches its 7-Stop.
Click any node to explore its meaning.
Four states that fall outside the six base rotations — at the STOP threshold, above resolution, or below the Natural State.
The Activator quantum (0.000001) is not a flat "+1 per Hard Stop." It carries the intention behind the stop — weighted by the resulting action, or the lack of one. The signed-integer scale −1 / 0 / +1 / +2 is taken directly from the Gravity Framework (§3.1, "The Four Intent States, mapped to a signed integer scale"); the +3 rung (Mercy) extends it to the maximum, drawing on the Intent Topology's highest operation (§2C — restoring a collapsed node from the Love register). Every Hard Stop deposits its weight into STOR, and under Information-Centric Gravitation the accumulated weight is the loop's mass. This is where "intention governs mechanics" stops being a slogan and becomes an equation.
Set every weight to +1 and the weighted law collapses back to STOR(k) = k × 0.000001 exactly.
That is why the nuclear binding-energy numbers in the Clasp Engine and NOS Calculator are unchanged:
a nucleus resolving its own register is pure +1 (Self) intent.
The weighting doesn't overwrite the physics — it reveals that the physics was living on a single rung
(+1) of a wider ladder. Move off that rung and you leave the domain of inert matter and enter the domain
the corpus reserves for directed intent: −1 removes weight (destructive), +2 propagates it
(Love / gravitational binding energy), +3 restores a collapsed node (Mercy).
Descent is cheap, ascent is dear: one −1 subtraction drops a loop to Hate; climbing to Love requires
building weight across the full cycle. The ladder is deliberately asymmetric, matching the Intent Topology's
"asymmetry of ascent and descent."
Click a weight to add one Hard Stop of that intent to the ledger. Watch raw STOR, weighted STOR, and the net field weight (mass contribution) diverge.
| Theorem | Statement |
|---|---|
| Maximum Period | Period of 1/7 in base 10 is exactly 6 (Fermat's Little Theorem: 10⁶ ≡ 1 mod 7) |
| Cyclic Permutations | 142857 × n (n=1…6) produces all six cyclic rotations — no new digits |
| 7th Multiple | 7 × 142857 = 999999 exactly — the Hard Stop |
| Complement-to-9 | Pairs {1,8}, {4,5}, {2,7} — positions i and i+3 sum to 9 |
| Group Structure | (ℤ/7ℤ)× is cyclic of order 6, generated by 3 ≡ 10 (mod 7) |
| Minimality | 142857 is the smallest cyclic number in base 10; 7 is the smallest full-reptend prime |
| Shannon Entropy | The 6 digits achieve maximum entropy log₂(6) ≈ 2.585 bits for a 6-state system |
Physical mass is a function of informational potential (Σ_STOR) resolved through the discrete Intent Activator (+0.000001). Empirically validated via the chemical triad of life (O, H, Fe) and the proton-to-electron mass ratio (1836), yielding compound p < 10⁻⁹.
The mathematical core is proven. The extended framework — gravity, intent topology, cosmological predictions — is a structured research proposal at the stage of qualitative mapping and internal coherence. Specific falsifiable predictions have not yet been independently tested.
This work is an invitation: test, challenge, build.
Intent-weight context: every resolution shown here is a +1 (Self) event on the Intent Weight ladder — a nucleus resolving its own register. That is why the mass-defect and binding-energy figures are ordinary, verified nuclear physics: they sit on the +1 rung, where weighted STOR equals classical STOR. The −1/+2/+3 rungs (Hate / Love / Mercy) apply to directed intent between loops, not to a nucleus binding to itself.
| Component | Count | Unit Mass | Total (u) |
|---|
Oxygen-16 has 8 protons + 8 neutrons + 8 electrons — the number 8 appears at every level.
In the 142857 cycle, 8 is the first digit of the Heavy Register (1→4→2→8→5→7),
the point where the loop crosses from the informational (142) half into the mass-bearing (857) half.
The 8-fold symmetry of O-16 makes it the ideal
clasp demonstration: the register that must absorb the maximum external activation
before resolving.
The 2+6 valence shell (2 inner electrons, 6 outer) maps onto the NOS cycle: the 2 inner-shell electrons correspond to the first two positions of the Light Register (1 and 4), while the 6 outer-shell electrons span one complete 6-position loop (1→4→2→8→5→7).
1. V_obs = 8(1.00728) + 8(1.00866) + 8(0.000549) = 16.1319 u
2. Σ_STOR = mass defect = 16.13192 − 15.99492 = 0.13700 u
3. ε_Activator fires: strong nuclear force supplies the +0.000001 NOS equivalent
4. N(r)_clasp = 17 × k rectifies the dimensional gap
5. V_target = 15.99491 u — loop closes (Hard Stop)
6. STOR energy (0.13700 u × 931.5 MeV/u) = 127.6 MeV photon
The mass-register resolves. The residue emits as a gamma photon.
This is the 1/7 loop's "Resolved Truth" — the integer 1 expressed as massless light.
The proton-to-electron mass ratio 1836 = 27 × 68 = 27 × (4 × 17).
27 is the Supervisory Gate — the invariant digit sum of the base register (1+4+2+8+5+7 = 27).
68 is the "68 Scale Matrix": four primary constants the corpus defines for physical
manifestation (Token Density, Vector Velocity, Contextual Gravity, Modular Parity)
multiplied by the 17 Scale Constant. The corpus treats this factorization as the
first-principles derivation of the ratio, rather than an unexplained measured constant.
Iron (Fe-56) sits at the peak of the nuclear binding energy curve — the most stable nucleus per nucleon (real physics, independent of the corpus). In NOS terms, this is the ultimate Hard Stop of atomic register accumulation, by analogy to how digit 7 is the Hard Stop of the base 142857 cycle. Elements lighter than Fe release energy by fusion; heavier elements release energy by fission. The documented Triad of Life plays three distinct roles: H is the Supervisory Bridge element (mass defect = 27²), O is the canonical Clasp (mass gap = the 999 register union), and Fe is the Hard Stop of the atomic-mass scale.
Water (H₂O) formation requires three discrete Hard Stop events — three activator firings at three different scales. Each resolved register passes its coherence to the next scale. The molecule does not form from raw nucleons — it forms from already-resolved atomic registers meeting at the molecular scale.
8 protons, 8 neutrons, 8 electrons (O) and 2 protons, 2 electrons (H×2) are present as fully dispersed sub-registers. Each nucleon runs the 1→4→2→8→5→7 loop independently. No Hard Stop has fired at any scale yet. The O register is accumulating maximum STOR (digit 8 — first digit of the Heavy Register). The H registers sit at digit 1 — Base Norm, waiting.
1: O nuclear Hard Stop — 127.6 MeV gamma
2: H(1) electron binding — 13.6 eV UV
3: H(2) electron binding — 13.6 eV UV
4: O-H bond 1 formation — 5.17 eV IR
5: O-H bond 2 formation — 5.17 eV IR
Total photon energy released on the path from raw nucleons to H₂O:
127.6 MeV + 27.2 eV + 10.34 eV
The NOS loop resolves at five distinct Hard Stops across three scales.
The +0.000001 Activator is scale-invariant — it fires at every Hard Stop regardless of the energy scale at which the loop is running. At each scale the energy unit changes, but the informational structure (0.142857, the 13-window, the Hard Stop) is identical. Click any scale to explore.
Intent-weight context: this calculator resolves each nucleus on its own — the +1 (Self) rung of the Intent Weight ladder, where weighted STOR equals classical STOR. So the mass defects and binding energies below are standard nuclear physics, unaffected by the signed intent model. Directed-intent weights (−1 Hate, +2 Love, +3 Mercy) act between loops, not within a self-binding nucleus.