Pith Number

pith:FNJOWWSY

pith:2025:FNJOWWSYEMC4EPUPEFCDGFKW6A

not attested not anchored not stored refs pending

Random Cayley graphs and random sumsets

Huy Tuan Pham, Noga Alon

arxiv:2509.02561 v1 · 2025-09-02 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNJOWWSYEMC4EPUPEFCDGFKW6A}

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.

Cited by

2 papers in Pith

Coloring sparse random Cayley graphs

Sumsets of random sets

Receipt and verification

First computed	2026-07-05T12:03:41.057875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b52eb5a582305c23e8f2144331556f02fdf6d91d2711e5fd331e0bf42b895c1

Aliases

arxiv: 2509.02561 · arxiv_version: 2509.02561v1 · doi: 10.48550/arxiv.2509.02561 · pith_short_12: FNJOWWSYEMC4 · pith_short_16: FNJOWWSYEMC4EPUP · pith_short_8: FNJOWWSY

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/FNJOWWSYEMC4EPUPEFCDGFKW6A \
  | 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: 2b52eb5a582305c23e8f2144331556f02fdf6d91d2711e5fd331e0bf42b895c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec3df329b022df9215b7ce0ce0c1d9f4131cf4459e183854c88675ba736559b2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-02T17:56:07Z",
    "title_canon_sha256": "d43516c5d4f83ccd846aaca6076fc9b1a3fc174539f029367a8dcc476e1bd56f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.02561",
    "kind": "arxiv",
    "version": 1
  }
}