Pith Number

pith:YHMU2VES

pith:2015:YHMU2VES7JNKLMF54RY2EJ4KDY

not attested not anchored not stored refs pending

Entropy Chaos and Bose-Einstein Condensation

Francesco C. De Vecchi, Sergio Albeverio, Stefania Ugolini

arxiv:1512.04729 v1 · 2015-12-15 · math.PR · math-ph · 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{YHMU2VES7JNKLMF54RY2EJ4KDY}

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	2026-05-18T01:24:15.731477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1d94d5492fa5aa5b0bde471a2278a1e33b28e0b01404dbd592ac4a2b8dadefa

Aliases

arxiv: 1512.04729 · arxiv_version: 1512.04729v1 · doi: 10.48550/arxiv.1512.04729 · pith_short_12: YHMU2VES7JNK · pith_short_16: YHMU2VES7JNKLMF5 · pith_short_8: YHMU2VES

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/YHMU2VES7JNKLMF54RY2EJ4KDY \
  | 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: c1d94d5492fa5aa5b0bde471a2278a1e33b28e0b01404dbd592ac4a2b8dadefa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5feb1c980f0a7cefe88acaca4048dd1c6df3ff5c4ad81b59d7d5e85398caa0fb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-15T11:19:11Z",
    "title_canon_sha256": "225aacf91c0e4fd6a8aeb115700a4d0074acab1aebabe9053b6d4789bee71159"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04729",
    "kind": "arxiv",
    "version": 1
  }
}