Pith Number

pith:2OAI4K4C

pith:2011:2OAI4K4CW6PJIJA6NX5FL3K2L6

not attested not anchored not stored refs pending

Some properties of the "String gas" with the equation of state $p = -\rho/3$

Alexander Yu. Kamenshchik, Isaak M. Khalatnikov

arxiv:1109.0201 v1 · 2011-09-01 · 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{2OAI4K4CW6PJIJA6NX5FL3K2L6}

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	2026-05-18T02:00:43.262951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3808e2b82b79e94241e6dfa55ed5a5f8576f6914e6ffd19edf53d91232b48ab

Aliases

arxiv: 1109.0201 · arxiv_version: 1109.0201v1 · doi: 10.48550/arxiv.1109.0201 · pith_short_12: 2OAI4K4CW6PJ · pith_short_16: 2OAI4K4CW6PJIJA6 · pith_short_8: 2OAI4K4C

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/2OAI4K4CW6PJIJA6NX5FL3K2L6 \
  | 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: d3808e2b82b79e94241e6dfa55ed5a5f8576f6914e6ffd19edf53d91232b48ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e0bca5103bfea604c55b95cb4be47184542a8a371d7ae149c2b3ca1e5b1af2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-09-01T14:52:55Z",
    "title_canon_sha256": "ad14a6f780acb1aefb4f43e5b8ccda67aa6a337083e625c604f11adea97e905b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0201",
    "kind": "arxiv",
    "version": 1
  }
}