Pith Number

pith:KFLAT5N5

pith:2024:KFLAT5N5YIKAUNTWIHKQZ452NI

not attested not anchored not stored refs pending

Sharp Thresholds for Factors in Random Graphs

Annika Heckel, Fabian Burghart, Marc Kaufmann, Matija Pasch, Noela M\"uller

arxiv:2411.14138 v2 · 2024-11-21 · math.CO · 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{KFLAT5N5YIKAUNTWIHKQZ452NI}

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	2026-07-05T11:52:16.090038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

515609f5bdc2140a367641d50cf3ba6a300daeb25b74adc52d49804c6a514184

Aliases

arxiv: 2411.14138 · arxiv_version: 2411.14138v2 · doi: 10.48550/arxiv.2411.14138 · pith_short_12: KFLAT5N5YIKA · pith_short_16: KFLAT5N5YIKAUNTW · pith_short_8: KFLAT5N5

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/KFLAT5N5YIKAUNTWIHKQZ452NI \
  | 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: 515609f5bdc2140a367641d50cf3ba6a300daeb25b74adc52d49804c6a514184

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89174340ba19f27651e44b0389001d027d356bfe684cefdf061eb463e549192a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-11-21T14:02:22Z",
    "title_canon_sha256": "cf2407333bc4200bcf36677922d9f207636f2bb70b234fe2db27d643cb167c7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.14138",
    "kind": "arxiv",
    "version": 2
  }
}