Pith Number

pith:7FUB4LWB

pith:2011:7FUB4LWBLBXZBK4RA6AJTG5JK7

not attested not anchored not stored refs pending

The general Friedmann equation: a mathematical point of view

Hellmut Baumg\"artel

arxiv:1110.0912 v1 · 2011-10-05 · astro-ph.CO · 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{7FUB4LWBLBXZBK4RA6AJTG5JK7}

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	2026-05-18T04:11:40.193408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9681e2ec1586f90ab910780999ba957ceb050afbe2fa6dd82abc6935dc00c65

Aliases

arxiv: 1110.0912 · arxiv_version: 1110.0912v1 · doi: 10.48550/arxiv.1110.0912 · pith_short_12: 7FUB4LWBLBXZ · pith_short_16: 7FUB4LWBLBXZBK4R · pith_short_8: 7FUB4LWB

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/7FUB4LWBLBXZBK4RA6AJTG5JK7 \
  | 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: f9681e2ec1586f90ab910780999ba957ceb050afbe2fa6dd82abc6935dc00c65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08f1ca7af1ecaac8514c805c7ebe2206dbddb6e818110df28267e1634b3f045e",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-10-05T07:33:08Z",
    "title_canon_sha256": "0f47146334d903d6c8aa7480cc0ef3fd497329826f3f49b10ccb0149f193e613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0912",
    "kind": "arxiv",
    "version": 1
  }
}