Pith Number

pith:3EEVP7WZ

pith:2026:3EEVP7WZWY7W3CE6EZH3RPBB6D

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Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes

Rajib Saha, Sukanta Panda, Tanay Gupta

Thurston spacetimes generate distinct time-evolving quadrupole patterns in CMB temperature and polarization via Stokes parameters.

arxiv:2605.14572 v1 · 2026-05-14 · gr-qc

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Record completeness

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Claims

C1strongest claim

We show the evolution of temperature and polarization amplitudes in terms of such Stokes parameters at different timestamps and attempt to isolate individual Thurston geometries.

C2weakest assumption

That Thurston spacetimes can be used as viable background geometries for the universe while producing coherent, distinguishable CMB signals without additional assumptions about initial conditions or matter content in the anisotropic setting.

C3one line summary

Thurston spacetimes generate distinct evolving temperature and polarization patterns in the CMB that can be tracked via Stokes parameters and potentially isolated per geometry.

References

74 extracted · 74 resolved · 7 Pith anchors

[1] Solv These eight maximal geometries can be said to form the building blocks of all compact 3-manifolds and are referred to asThurston geometries. These are:

[2] FLRW spacetimes R3/H3/S3 (3) ds2 =−dt 2 +a 2(t){dχ2 +S 2 κ(χ)dΩ2}(2.1)

[3] FLRW spacetimes in 2D with a third flat anisotropic axis R×H 2/S2 (2) ds2 =−dt 2 +a 2(t){dz2 +dχ 2 +S 2 κ(χ)dϕ2}(2.2) {z∈R is orthogonal to (χ,ϕ) plane} where Sκ(χ) =    sin(χ√κ)√κ , κ >0 (S 3,

[4] Universal cover of the unit tangent bundle of the hyperbolic plane ^U(H2) (1) ds2 =−dt 2 +a 2(t) n dx2 + cosh2 x √ −κ dy2 + dz+ sinh x √ −κ dy 2o (2.5)

[5] Nilpotent subgroup of an extension of the group of isometries (abb.Nil)(1) ds2 =−dt 2 +a 2(t) dx2 + 1−κ x 2 dy2 +dz 2 −2x √ −κ dy dz (2.6)

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:05.460706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d90957fed9b63f6d889e264fb8bc21f0f4fae09b93740fe7ca173b2664fc97d0

Aliases

arxiv: 2605.14572 · arxiv_version: 2605.14572v1 · doi: 10.48550/arxiv.2605.14572 · pith_short_12: 3EEVP7WZWY7W · pith_short_16: 3EEVP7WZWY7W3CE6 · pith_short_8: 3EEVP7WZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3EEVP7WZWY7W3CE6EZH3RPBB6D \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d90957fed9b63f6d889e264fb8bc21f0f4fae09b93740fe7ca173b2664fc97d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0af73b759f7a8480be65b56da9d51e46da2e5f9a59ed563b367288b4de7ece61",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-14T08:43:08Z",
    "title_canon_sha256": "2acaaa7477bf11ac386b4aa45839b998e2d3aed85c54edbf1aa07a0c2329efd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14572",
    "kind": "arxiv",
    "version": 1
  }
}