Pith Number

pith:D4F527YV

pith:2013:D4F527YVM5KSGP37EFTMJ65NXU

not attested not anchored not stored refs pending

An inductive proof of Straub's q-analogue of Ljunggren's congruence

Bo Ning

arxiv:1301.2986 v2 · 2013-01-14 · 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{D4F527YVM5KSGP37EFTMJ65NXU}

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	2026-05-18T03:36:03.802382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f0bdd7f156755233f7f2166c4fbadbd153bb821ee6d043225db8d62439647fe

Aliases

arxiv: 1301.2986 · arxiv_version: 1301.2986v2 · doi: 10.48550/arxiv.1301.2986 · pith_short_12: D4F527YVM5KS · pith_short_16: D4F527YVM5KSGP37 · pith_short_8: D4F527YV

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/D4F527YVM5KSGP37EFTMJ65NXU \
  | 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: 1f0bdd7f156755233f7f2166c4fbadbd153bb821ee6d043225db8d62439647fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68326e5b2031a6b98356c9d890d3b03b35dd637764a3d767b20d93372ba26e8a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-01-14T14:25:54Z",
    "title_canon_sha256": "9a3f6b967e49d91f22adaffd796be3f1ab9a3d4ef589be2c0629f04447ef0d57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2986",
    "kind": "arxiv",
    "version": 2
  }
}