ICHIMPRINTED CURVATURE HYPOTHESIS
Imprinted Curvature Hypothesis

What if spacetime
remembers?

A conservative geometric question inside unmodified General Relativity.

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LATEST RELEASEICH V4RELEASED · 05 SEP 2026

From framework
to mathematical formulation.

V4 consolidates ICH as a mathematically explicit, GR-consistent initial-condition hypothesis, with constraint-satisfying ADM initial data, gauge-safe long-mode treatment, unified observable forward equations, and numerical validation using CAMB, CLASS and Planck PR3 data.

41-page consolidated manuscriptReproducibility code includedRELEASED
The Planck low-ℓ benchmark is non-confirmatory and compatible with the null hypothesis (global p = 0.454 ± 0.011).
Download consolidated manuscript PDF · 41 PAGESOpen archival record ZENODO ↗Download code directly ZIP · 20 KBPublication record
NO NEW SECTOR

No new particles.

The hypothesis introduces no additional matter species, no propagating field and no hidden dynamical sector.

UNMODIFIED GR

No modified gravity.

The Einstein field equations and standard matter conservation remain intact. Exact FLRW is recovered when the imprint amplitude tends to zero.

INITIAL GEOMETRY

A weak primordial imprint.

ICH asks whether ultra-long-wavelength curvature information can be admitted as initial spatial data and persist as a frozen large-scale bias.

OBSERVATIONAL SIGNATURE

Weak. Smooth. Statistical.

Any valid signal must remain coherent on the largest scales—never a sharp local mass clump, a dominant correction or a freely adjustable explanation.

ONE IMPRINT · THIRTEEN TESTS

Not a catalogue of anomalies.
A restricted pattern that can fail.

P11 + P12 · ICONIC NODE-ENVIRONMENT SIGNATURE

The Cosmic Giant’s
Two Faces.

ICH proposes two observable faces of the same broader node-linked extreme-growth channel. This is a population-level contrast test—not a claim that both faces must appear in one object.

P11 · RADIANT PHASE

The giant burns.

Massive Euclid-defined nodes should show a residual excess in the extreme luminous-quasar or active ultra-massive-black-hole tail after standard astrophysical controls.

Open P11
P12 · VEILED PHASE

The giant fades.

Comparable massive-node environments may host faded or low-accretion counterparts. Dark Nodes sharpen the test: high inferred mass and node-like topology, but weak light.

Open P12
P13 · THE BARYONIC TRACEAnd the cosmic web keeps the trace.Open P13
01P1–P5

Coherence

Stable across redshift. Subdominant in amplitude. Reproducible across independent surveys. Background expansion preserved.

Core tests
02P6–P10

Scale & selectivity

Smooth void response. No new local clumps. No small-scale imprint. Rare early growth and only faint anisotropy.

Large-scale tests
03P11–P13

The giant’s two faces

Radiant nodes, veiled or dark nodes, and the baryonic trace—tested as populations, never by famous objects alone.

Node tests
The decisive observational program

Predicted before
the data.

P1–P13 are preserved on the pre-DR1 side. Every later result belongs on the post-DR1 register—with its release, pipeline, controls, significance and verdict exposed.

Open Euclid DR1 protocol View observational context