Pith Number

pith:ZX5C7HHJ

pith:2014:ZX5C7HHJMKXVI6OGGWWGIVMFZO

not attested not anchored not stored refs pending

Modular symbols in Iwasawa theory

Kazuya Kato, Romyar Sharifi, Takako Fukaya

arxiv:1402.3850 v2 · 2014-02-16 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZX5C7HHJMKXVI6OGGWWGIVMFZO}

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	2026-05-18T02:30:01.217058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e

Aliases

arxiv: 1402.3850 · arxiv_version: 1402.3850v2 · doi: 10.48550/arxiv.1402.3850 · pith_short_12: ZX5C7HHJMKXV · pith_short_16: ZX5C7HHJMKXVI6OG · pith_short_8: ZX5C7HHJ

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/ZX5C7HHJMKXVI6OGGWWGIVMFZO \
  | 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: cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3214505f08013b1630fd07129e9db9b49defa7abb58ce42cec81332b2187fb7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-02-16T22:26:49Z",
    "title_canon_sha256": "b07b3f4ed113d8144a037432ec106f0957e940bc273312f19e615311c813efb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.3850",
    "kind": "arxiv",
    "version": 2
  }
}