Pith Number

pith:PDW52EI3

pith:2018:PDW52EI3T2AUKR4S3LZ25TAALW

not attested not anchored not stored refs pending

Breaking of ensemble equivalence for perturbed Erd\H{o}s-R\'enyi random graphs

A. Roccaverde, F. den Hollander, M. Mandjes, N.J. Starreveld

arxiv:1807.07750 v4 · 2018-07-20 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDW52EI3T2AUKR4S3LZ25TAALW}

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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.

Cited by

1 paper in Pith

Emergence in graphs with near-extreme constraints

Receipt and verification

First computed	2026-07-05T02:48:31.304234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78eddd111b9e81454792daf3aecc005d898aff708f7b8eacc60f034177dcab28

Aliases

arxiv: 1807.07750 · arxiv_version: 1807.07750v4 · doi: 10.48550/arxiv.1807.07750 · pith_short_12: PDW52EI3T2AU · pith_short_16: PDW52EI3T2AUKR4S · pith_short_8: PDW52EI3

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/PDW52EI3T2AUKR4S3LZ25TAALW \
  | 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: 78eddd111b9e81454792daf3aecc005d898aff708f7b8eacc60f034177dcab28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05aad9b82b3a5aeb6a7703c5c754637b16a9d01434374506ff2ec168ac419d59",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-07-20T09:09:36Z",
    "title_canon_sha256": "15d683af49f16419c7effcda1478900391dde35b543f954b6dac7742ab13da2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.07750",
    "kind": "arxiv",
    "version": 4
  }
}