Pith Number

pith:36HNETUT

pith:2024:36HNETUTCK7GBKAHKB5QK43USG

not attested not anchored not stored refs pending

Note on a conjecture of Talagrand: expectation thresholds vs. fractional expectation thresholds

Jeff Kahn, Jinyoung Park, Quentin Dubroff

arxiv:2412.00917 v1 · 2024-12-01 · math.CO · math.PR

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\usepackage{pith}
\pithnumber{36HNETUTCK7GBKAHKB5QK43USG}

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Record completeness

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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

Further remarks on fractional vs. expectation thresholds

Receipt and verification

First computed	2026-07-05T09:42:50.391820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df8ed24e9312be60a807507b05737491ad750c75bd192c923faf3e27569c8ffd

Aliases

arxiv: 2412.00917 · arxiv_version: 2412.00917v1 · doi: 10.48550/arxiv.2412.00917 · pith_short_12: 36HNETUTCK7G · pith_short_16: 36HNETUTCK7GBKAH · pith_short_8: 36HNETUT

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/36HNETUTCK7GBKAHKB5QK43USG \
  | 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: df8ed24e9312be60a807507b05737491ad750c75bd192c923faf3e27569c8ffd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d93563328d6848e5866678f9da54f94e42a44c2e42fbe22bf6add09a4bb2f8f0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-01T18:06:07Z",
    "title_canon_sha256": "d63ccd74baceaf3f5ebf7689e24ff87cd569fcd8b7134390567215e8a2789b05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.00917",
    "kind": "arxiv",
    "version": 1
  }
}