Pith Number

pith:PBEU6A7E

pith:2025:PBEU6A7EM65NCTO3WQEK4H73GX

not attested not anchored not stored refs pending

When does a tree activate the random graph?

Asaf Cohen Antonir, Asaf Shapira, Maksim Zhukovskii, Mykhaylo Tyomkyn, Yuval Peled

arxiv:2507.05697 v1 · 2025-07-08 · math.CO · math.AT · 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{PBEU6A7EM65NCTO3WQEK4H73GX}

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.

Cited by

1 paper in Pith

Weak saturation numbers of large complete bipartite graphs

Receipt and verification

First computed	2026-07-05T11:33:34.929559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78494f03e467bad14ddbb408ae1ffb35c1abd4123dac52fd6937f9c8b5b6d516

Aliases

arxiv: 2507.05697 · arxiv_version: 2507.05697v1 · doi: 10.48550/arxiv.2507.05697 · pith_short_12: PBEU6A7EM65N · pith_short_16: PBEU6A7EM65NCTO3 · pith_short_8: PBEU6A7E

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/PBEU6A7EM65NCTO3WQEK4H73GX \
  | 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: 78494f03e467bad14ddbb408ae1ffb35c1abd4123dac52fd6937f9c8b5b6d516

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d07856abf2695be153337ffed2837f9b354c79ff2ff1e5ae70d12ea1d4a2f85d",
    "cross_cats_sorted": [
      "math.AT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-08T06:09:01Z",
    "title_canon_sha256": "1511824b9fc4b50b2661f1e37bd78b4b0ce11294a43183735fa5d1d635ec50ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.05697",
    "kind": "arxiv",
    "version": 1
  }
}