Pith Number

pith:FFRIMMYK

pith:2011:FFRIMMYKOOVYRTW2L3V2MMMHGM

not attested not anchored not stored refs pending

p-adic congruences motivated by series

Zhi-Wei Sun

arxiv:1111.4988 v4 · 2011-11-21 · math.NT · 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{FFRIMMYKOOVYRTW2L3V2MMMHGM}

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	2026-05-18T03:05:44.985410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

296286330a73ab88ceda5eeba6318733244f5d9edb3d0ea4c297e5a22570526a

Aliases

arxiv: 1111.4988 · arxiv_version: 1111.4988v4 · doi: 10.48550/arxiv.1111.4988 · pith_short_12: FFRIMMYKOOVY · pith_short_16: FFRIMMYKOOVYRTW2 · pith_short_8: FFRIMMYK

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/FFRIMMYKOOVYRTW2L3V2MMMHGM \
  | 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: 296286330a73ab88ceda5eeba6318733244f5d9edb3d0ea4c297e5a22570526a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c5fbcbb0e1f0e4b84812c11657850389d80a70f433c6bfcc40be7af2f086c65",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-21T19:58:22Z",
    "title_canon_sha256": "a94d866e35f8ceb9da7b3a942ca2b4a26f204b0e38d4da92ab3c1ebeb20c1b83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4988",
    "kind": "arxiv",
    "version": 4
  }
}