Pith Number

pith:VYAJV3K7

pith:2024:VYAJV3K7HPVAZGNCQRGNKRWBYC

not attested not anchored not stored refs pending

Asymptotically Optimal Threshold Bias for the $(a : b)$ Maker-Breaker Minimum Degree, Connectivity and Hamiltonicity Games

Adnane Fouadi, Anand Srivastav, Mourad El Ouali

arxiv:2406.11051 v1 · 2024-06-16 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYAJV3K7HPVAZGNCQRGNKRWBYC}

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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

Maker playing against an invisible Breaker

Receipt and verification

First computed	2026-07-05T08:32:48.167638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae009aed5f3bea0c99a2844cd546c1c0881225d22701c75d297db7e09e242624

Aliases

arxiv: 2406.11051 · arxiv_version: 2406.11051v1 · doi: 10.48550/arxiv.2406.11051 · pith_short_12: VYAJV3K7HPVA · pith_short_16: VYAJV3K7HPVAZGNC · pith_short_8: VYAJV3K7

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/VYAJV3K7HPVAZGNCQRGNKRWBYC \
  | 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: ae009aed5f3bea0c99a2844cd546c1c0881225d22701c75d297db7e09e242624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8b50ac0c148974ae7bed5be5f893ea17f24893c7f93f9a6f8c058895dea8a36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-06-16T19:24:53Z",
    "title_canon_sha256": "051fc24336c7ef66def42ea20397db6573862284e3119319c2c29e3b610e9265"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2406.11051",
    "kind": "arxiv",
    "version": 1
  }
}