Pith Number

pith:FWMX5MKF

pith:2010:FWMX5MKFXO2442TMBIZIZU6QV2

not attested not anchored not stored refs pending

Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

J\"org H\"arterich, Kevin Webster, Marc Georgi, Stefan Liebscher

arxiv:1004.1989 v3 · 2010-04-12 · gr-qc · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FWMX5MKFXO2442TMBIZIZU6QV2}

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	2026-05-18T04:22:01.046369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d997eb145bbb5ce6a6c0a328cd3d0ae894fbe43f0385d73d2185c15b7730f3a

Aliases

arxiv: 1004.1989 · arxiv_version: 1004.1989v3 · doi: 10.48550/arxiv.1004.1989 · pith_short_12: FWMX5MKFXO24 · pith_short_16: FWMX5MKFXO2442TM · pith_short_8: FWMX5MKF

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/FWMX5MKFXO2442TMBIZIZU6QV2 \
  | 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: 2d997eb145bbb5ce6a6c0a328cd3d0ae894fbe43f0385d73d2185c15b7730f3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34d6415ded53157ac75d72d5897efa6cf93816faa641754d5340e1e52f4ab154",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-04-12T15:32:05Z",
    "title_canon_sha256": "fee4e7a0293874eb54b02daf082ca58861a271228f35c822675eceec24e4fbfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1989",
    "kind": "arxiv",
    "version": 3
  }
}