Pith Number

pith:RR5WKFYW

pith:2024:RR5WKFYWIHWENWLHZMM7DNPPRN

not attested not anchored not stored refs pending

A sharp version of Talagrand's selector process conjecture and an application to rounding fractional covers

Huy Tuan Pham

arxiv:2412.03540 v1 · 2024-12-04 · math.CO · cs.DM · 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{RR5WKFYWIHWENWLHZMM7DNPPRN}

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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

Further remarks on fractional vs. expectation thresholds

Receipt and verification

First computed	2026-07-05T09:44:30.934718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c7b65171641ec46d967cb19f1b5ef8b6bfe4e2a61b4ac3198ebe33a4877cf9e

Aliases

arxiv: 2412.03540 · arxiv_version: 2412.03540v1 · doi: 10.48550/arxiv.2412.03540 · pith_short_12: RR5WKFYWIHWE · pith_short_16: RR5WKFYWIHWENWLH · pith_short_8: RR5WKFYW

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/RR5WKFYWIHWENWLHZMM7DNPPRN \
  | 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: 8c7b65171641ec46d967cb19f1b5ef8b6bfe4e2a61b4ac3198ebe33a4877cf9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbc2a70c0e26a94fb2e5889c297957dc5fb043ad87642427514a1498166a334f",
    "cross_cats_sorted": [
      "cs.DM",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-04T18:37:17Z",
    "title_canon_sha256": "6ae97b4fc3f671dfa6cd45e32623c58e7fe354b53df858a22a5ff8da81f0c89d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03540",
    "kind": "arxiv",
    "version": 1
  }
}