Pith Number

pith:DQ3T5RO6

pith:2024:DQ3T5RO6SZDOCU77DREMMMIRHP

not attested not anchored not stored refs pending

Upper tails for arithmetic progressions revisited

Frank Mousset, Matan Harel, Wojciech Samotij

arxiv:2409.08383 v1 · 2024-09-12 · math.PR · 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{DQ3T5RO6SZDOCU77DREMMMIRHP}

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	2026-07-05T09:06:30.313774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c373ec5de9646e153ff1c48c631113bd63d7ab8ebcf88d6e80aeff84512ce37

Aliases

arxiv: 2409.08383 · arxiv_version: 2409.08383v1 · doi: 10.48550/arxiv.2409.08383 · pith_short_12: DQ3T5RO6SZDO · pith_short_16: DQ3T5RO6SZDOCU77 · pith_short_8: DQ3T5RO6

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/DQ3T5RO6SZDOCU77DREMMMIRHP \
  | 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: 1c373ec5de9646e153ff1c48c631113bd63d7ab8ebcf88d6e80aeff84512ce37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd06c8ab2df243d0c7eaa4c20ed05a0eeeb74daeacc726d29fc437f8e2b909e1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-09-12T20:17:48Z",
    "title_canon_sha256": "3e7c146d2faa9dc18e6e4a12537aa16e2924e257cdee1882aa8e76314242ddeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.08383",
    "kind": "arxiv",
    "version": 1
  }
}