Pith Number

pith:6RFO6K7H

pith:2012:6RFO6K7HUZTXCYWOG6FLCHFLU2

not attested not anchored not stored refs pending

Shintani cocycles and vanishing order of $p$-adic Hecke $L$-series at $s=0$

Michael Spiess

arxiv:1203.6689 v3 · 2012-03-30 · 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{6RFO6K7HUZTXCYWOG6FLCHFLU2}

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	2026-05-18T03:51:23.412589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f44aef2be7a6677162ce378ab11caba682bbf8a65a01ede18cd54f7ff9217976

Aliases

arxiv: 1203.6689 · arxiv_version: 1203.6689v3 · doi: 10.48550/arxiv.1203.6689 · pith_short_12: 6RFO6K7HUZTX · pith_short_16: 6RFO6K7HUZTXCYWO · pith_short_8: 6RFO6K7H

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/6RFO6K7HUZTXCYWOG6FLCHFLU2 \
  | 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: f44aef2be7a6677162ce378ab11caba682bbf8a65a01ede18cd54f7ff9217976

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9498999d028eadabd32f24ec91ffb514940e3c5c57d1dc8ace7272f5052f0229",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-30T00:17:48Z",
    "title_canon_sha256": "49d107bf9a75ea77ee127fc55280cb570b9e4d4a04c05e4b06913b31496a8d38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6689",
    "kind": "arxiv",
    "version": 3
  }
}