Pith Number

pith:NHH5UI6S

pith:2007:NHH5UI6SFDT5QWLEIHELMT5FLB

not attested not anchored not stored refs pending

Symmetry p-adic invariant integral on Z_p for Bernoulli and euler polynomials

T. Kim

arxiv:0712.0138 v1 · 2007-12-02 · 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{NHH5UI6SFDT5QWLEIHELMT5FLB}

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	2026-07-04T15:06:00.417081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69cfda23d228e7d8596441c8b64fa558484126aba3844df1946d0b09c5363cd8

Aliases

arxiv: 0712.0138 · arxiv_version: 0712.0138v1 · doi: 10.48550/arxiv.0712.0138 · pith_short_12: NHH5UI6SFDT5 · pith_short_16: NHH5UI6SFDT5QWLE · pith_short_8: NHH5UI6S

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/NHH5UI6SFDT5QWLEIHELMT5FLB \
  | 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: 69cfda23d228e7d8596441c8b64fa558484126aba3844df1946d0b09c5363cd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40a19cc7c32a5d1317888c3cd1ae55ee8773a2dfddc2cbb88dde937bde8111c4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-12-02T12:02:15Z",
    "title_canon_sha256": "3aff7c1fb322fca3e1ee0ed8f9924b712cec1e29830ab299e57ef47f7e4f99bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.0138",
    "kind": "arxiv",
    "version": 1
  }
}