Pith Number

pith:PI52AX5M

pith:2011:PI52AX5MVBALBB3Q5U3XD5WPWS

not attested not anchored not stored refs pending

A q-analog of Ljunggren's binomial congruence

Armin Straub

arxiv:1103.3258 v1 · 2011-03-16 · 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{PI52AX5MVBALBB3Q5U3XD5WPWS}

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	2026-05-18T04:26:44.491334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a3ba05faca840b08770ed3771f6cfb495fd5b977faadc483495a2aea7dd7907

Aliases

arxiv: 1103.3258 · arxiv_version: 1103.3258v1 · doi: 10.48550/arxiv.1103.3258 · pith_short_12: PI52AX5MVBAL · pith_short_16: PI52AX5MVBALBB3Q · pith_short_8: PI52AX5M

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/PI52AX5MVBALBB3Q5U3XD5WPWS \
  | 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: 7a3ba05faca840b08770ed3771f6cfb495fd5b977faadc483495a2aea7dd7907

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86cfc68d85ec5f7f78557ecee72768cde48175dc0fe35cfc41b220a5e25632ea",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-16T19:04:29Z",
    "title_canon_sha256": "72771ac64849f7f19317af49669e30985e940224d8d8d585e4feabd7dc6c84cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3258",
    "kind": "arxiv",
    "version": 1
  }
}