Pith Number

pith:THVMMBN2

pith:2026:THVMMBN2DNDWJ47DJKS73QYW4X

not attested not anchored not stored refs pending

Spectrum of Directed Inhomogeneous Random Graphs

Giacomo Passuello, Rajat Subhra Hazra

arxiv:2607.08696 v1 · 2026-07-09 · 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{THVMMBN2DNDWJ47DJKS73QYW4X}

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	2026-07-10T01:19:57.776819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99eac605ba1b4764f3e34aa5fdc316e5c0da4aabd06aeda3882065b4691ccc57

Aliases

arxiv: 2607.08696 · arxiv_version: 2607.08696v1 · doi: 10.48550/arxiv.2607.08696 · pith_short_12: THVMMBN2DNDW · pith_short_16: THVMMBN2DNDWJ47D · pith_short_8: THVMMBN2

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/THVMMBN2DNDWJ47DJKS73QYW4X \
  | 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: 99eac605ba1b4764f3e34aa5fdc316e5c0da4aabd06aeda3882065b4691ccc57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191c1375c7fd52fcea06027c6d687b9cc4522eaf8b124954480dba75ff3a7147",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-09T16:53:19Z",
    "title_canon_sha256": "3964ced56896f63e57aada46cecc266c0cd195af909a1f422ed091dda09f497d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08696",
    "kind": "arxiv",
    "version": 1
  }
}