Pith Number

pith:S2RNIGOF

pith:2015:S2RNIGOFXYWPFYT34DR7YAWVVZ

not attested not anchored not stored refs pending

Modular symbols and the integrality of zeta elements

Kazuya Kato, Romyar Sharifi, Takako Fukaya

arxiv:1507.00495 v2 · 2015-07-02 · 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{S2RNIGOFXYWPFYT34DR7YAWVVZ}

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	2026-05-18T01:04:46.620562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96a2d419c5be2cf2e27be0e3fc02d5ae7fa68fd5b20837d683ec3480f6f712a2

Aliases

arxiv: 1507.00495 · arxiv_version: 1507.00495v2 · doi: 10.48550/arxiv.1507.00495 · pith_short_12: S2RNIGOFXYWP · pith_short_16: S2RNIGOFXYWPFYT3 · pith_short_8: S2RNIGOF

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/S2RNIGOFXYWPFYT34DR7YAWVVZ \
  | 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: 96a2d419c5be2cf2e27be0e3fc02d5ae7fa68fd5b20837d683ec3480f6f712a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d43cdcc31e1bbf5b161d289b72cfe245c404a305f03eef83a89fb8720363532",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-07-02T09:55:38Z",
    "title_canon_sha256": "d6b8787b4f06a435bf1db85af61b4e5e34da5d9618b5705878c859d15f5dff6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00495",
    "kind": "arxiv",
    "version": 2
  }
}