Pith Number

pith:XIBAU6XX

pith:2015:XIBAU6XXPCL4F5IO7ZUL4KRBKP

not attested not anchored not stored refs pending

Mean-field limit and phase transitions for nematic liquid crystals in the continuum

Fran\c{c}ois Genoud, Sven Bachmann

arxiv:1508.05025 v4 · 2015-08-20 · math-ph · cond-mat.stat-mech · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XIBAU6XXPCL4F5IO7ZUL4KRBKP}

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	2026-05-18T00:40:24.488451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba020a7af77897c2f50efe68be2a2153c04da768f69dd5a5c48f99531c7f03f6

Aliases

arxiv: 1508.05025 · arxiv_version: 1508.05025v4 · doi: 10.48550/arxiv.1508.05025 · pith_short_12: XIBAU6XXPCL4 · pith_short_16: XIBAU6XXPCL4F5IO · pith_short_8: XIBAU6XX

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/XIBAU6XXPCL4F5IO7ZUL4KRBKP \
  | 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: ba020a7af77897c2f50efe68be2a2153c04da768f69dd5a5c48f99531c7f03f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92b99e90ec04d8d01441545654f41c219e74ba4d3145cacd1e0074c0a542a38d",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-08-20T16:11:15Z",
    "title_canon_sha256": "a754650b9d40d0443b26b595f7251aeff440b1cd59b18f21742a47940ecb2b00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05025",
    "kind": "arxiv",
    "version": 4
  }
}