Pith Number

pith:JXPTDPDU

pith:2012:JXPTDPDULLR4FMNBPU5ZXAB7BC

not attested not anchored not stored refs pending

M24-twisted Product Expansions are Siegel Modular Forms

Martin Raum

arxiv:1208.3453 v4 · 2012-08-16 · 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{JXPTDPDULLR4FMNBPU5ZXAB7BC}

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	2026-05-18T03:26:23.063353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ddf31bc745ae3c2b1a17d3b9b803f08b8cbbf7f64451559ddebed7601fa4c1a

Aliases

arxiv: 1208.3453 · arxiv_version: 1208.3453v4 · doi: 10.48550/arxiv.1208.3453 · pith_short_12: JXPTDPDULLR4 · pith_short_16: JXPTDPDULLR4FMNB · pith_short_8: JXPTDPDU

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/JXPTDPDULLR4FMNBPU5ZXAB7BC \
  | 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: 4ddf31bc745ae3c2b1a17d3b9b803f08b8cbbf7f64451559ddebed7601fa4c1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "908ba451e26e1e57d039cedbc466d0be060e44be22fe90421cc62e745ad3c0b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-16T19:38:10Z",
    "title_canon_sha256": "5f6b45880634d09ecf586a9b492fd402a5ef21f9abac1befbb026482ee1f991e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3453",
    "kind": "arxiv",
    "version": 4
  }
}