Pith Number

pith:ZXC42MOP

pith:2019:ZXC42MOPPKKRAZ25BBPTTYB6FK

not attested not anchored not stored refs pending

Strong Kac's chaos in the mean-field Bose-Einstein Condensation

Andrea Romano, Francesco C. De Vecchi, Sergio Albeverio, Stefania Ugolini

arxiv:1903.07128 v1 · 2019-03-17 · 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{ZXC42MOPPKKRAZ25BBPTTYB6FK}

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	2026-07-05T01:23:53.736222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdc5cd31cf7a9510675d085f39e03e2aa30119dad6e6cb72296a4acd4a8c4e4b

Aliases

arxiv: 1903.07128 · arxiv_version: 1903.07128v1 · doi: 10.48550/arxiv.1903.07128 · pith_short_12: ZXC42MOPPKKR · pith_short_16: ZXC42MOPPKKRAZ25 · pith_short_8: ZXC42MOP

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/ZXC42MOPPKKRAZ25BBPTTYB6FK \
  | 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: cdc5cd31cf7a9510675d085f39e03e2aa30119dad6e6cb72296a4acd4a8c4e4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dea60491b1dad8cb186abf034e7725c905f1b31ee95b34720351d47bf3d76dbd",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-17T17:09:11Z",
    "title_canon_sha256": "8a1fe39175046185752df766b0b996ff79b8b56b280c48d3351742e0b1836c0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.07128",
    "kind": "arxiv",
    "version": 1
  }
}