Pith Number

pith:73WCYKY6

pith:2015:73WCYKY62UNC763MO5JJ66BXKI

not attested not anchored not stored refs pending

Singularity avoidance in a quantum model of the Mixmaster universe

Ewa Czuchry, Herv\'e Bergeron, Jean-Pierre Gazeau, Przemys{\l}aw Ma{\l}kiewicz, W{\l}odzimierz Piechocki

arxiv:1501.07871 v4 · 2015-01-30 · 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{73WCYKY62UNC763MO5JJ66BXKI}

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	2026-05-18T01:24:19.304863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

feec2c2b1ed51a2ffb6c77529f7837522b7ba9e93eec72bc5d73fce05fe39062

Aliases

arxiv: 1501.07871 · arxiv_version: 1501.07871v4 · doi: 10.48550/arxiv.1501.07871 · pith_short_12: 73WCYKY62UNC · pith_short_16: 73WCYKY62UNC763M · pith_short_8: 73WCYKY6

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/73WCYKY62UNC763MO5JJ66BXKI \
  | 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: feec2c2b1ed51a2ffb6c77529f7837522b7ba9e93eec72bc5d73fce05fe39062

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6799e1b3de42b4f23e49f4362827953f447c7408cde7f43914ea4d83f55d07f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-01-30T18:23:59Z",
    "title_canon_sha256": "9264813a3d1eb0009129b3376fb6a5b824c592cef4422ae99f5fb0893f66e6f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07871",
    "kind": "arxiv",
    "version": 4
  }
}