Pith Number

pith:PBANZTOU

pith:2010:PBANZTOUEYNZ2FH6CQ2NBZRSST

not attested not anchored not stored refs pending

Super congruences and Euler numbers

Zhi-Wei Sun

arxiv:1001.4453 v20 · 2010-01-25 · 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{PBANZTOUEYNZ2FH6CQ2NBZRSST}

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	2026-05-18T02:09:30.324788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7840dccdd4261b9d14fe1434d0e63294f49b0b687ff112e49bd2cf779fa7cd9a

Aliases

arxiv: 1001.4453 · arxiv_version: 1001.4453v20 · doi: 10.48550/arxiv.1001.4453 · pith_short_12: PBANZTOUEYNZ · pith_short_16: PBANZTOUEYNZ2FH6 · pith_short_8: PBANZTOU

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/PBANZTOUEYNZ2FH6CQ2NBZRSST \
  | 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: 7840dccdd4261b9d14fe1434d0e63294f49b0b687ff112e49bd2cf779fa7cd9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6b2aa5c38e5e8bd6e7e46936e58d5f1d06f4fcbbc54eccd57db56207d3b1bbb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-01-25T20:13:46Z",
    "title_canon_sha256": "be64bfb7be1a19ada4ca93d5ea514cdb9294a1e968d3bc6ae92987fc6ede145a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4453",
    "kind": "arxiv",
    "version": 20
  }
}