Pith Number

pith:Z7TDL3Q3

pith:2001:Z7TDL3Q326BKPPBA6EIBC7XLEN

not attested not anchored not stored refs pending

Has the Universe always expanded ?

Nelson Pinto-Neto (CBPF), Patrick Peter (IAP)

arxiv:gr-qc/0109038 v1 · 2001-09-11 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7TDL3Q326BKPPBA6EIBC7XLEN}

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.

Cited by

1 paper in Pith

Low-energy limit in the anomaly-induced action and the semiclassical cosmological bounce

Receipt and verification

First computed	2026-07-04T16:26:57.392504Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfe635ee1bd782a7bc20f110117eeb2351901a83e698a99a8ac109f85c006fbc

Aliases

arxiv: gr-qc/0109038 · arxiv_version: gr-qc/0109038v1 · doi: 10.48550/arxiv.gr-qc/0109038 · pith_short_12: Z7TDL3Q326BK · pith_short_16: Z7TDL3Q326BKPPBA · pith_short_8: Z7TDL3Q3

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/Z7TDL3Q326BKPPBA6EIBC7XLEN \
  | 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: cfe635ee1bd782a7bc20f110117eeb2351901a83e698a99a8ac109f85c006fbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b6ba115eaceab1d491fca745224e46c229e28d3f6128d24d982e7f86a82c0fe",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2001-09-11T16:35:10Z",
    "title_canon_sha256": "8409cd026fad4b52076d668d0ffb6caec6e3f242cf7b4ac5b956758b6b8a21b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0109038",
    "kind": "arxiv",
    "version": 1
  }
}