Pith Number

pith:L5UGQZGR

pith:2025:L5UGQZGRKZU4CYFVCD3MMESYIV

not attested not anchored not stored refs pending

Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework

Abhijit Bhattacharyya, Debashis Gangopadhyay, Eduardo Guendelman, Goutam Manna, Samit Ganguly

arxiv:2503.03076 v2 · 2025-03-05 · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5UGQZGRKZU4CYFVCD3MMESYIV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:16:06.745953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062

Aliases

arxiv: 2503.03076 · arxiv_version: 2503.03076v2 · doi: 10.48550/arxiv.2503.03076 · pith_short_12: L5UGQZGRKZU4 · pith_short_16: L5UGQZGRKZU4CYFV · pith_short_8: L5UGQZGR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV \
  | 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: 5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99004eaaefff36e4c00481a84fad861138119aef0725a7d0abc6053285c72ef3",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-03-05T00:31:42Z",
    "title_canon_sha256": "4465979e0de8eee0d5eb34f8ec5b6a27bbd44414e22a08f190055b0843569848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.03076",
    "kind": "arxiv",
    "version": 2
  }
}