Pith Number

pith:S5CZUZ5X

pith:2012:S5CZUZ5XBRNQIR4P7RDL3DSYOG

not attested not anchored not stored refs pending

Formulas for central critical values of twisted L-functions attached to paramodular forms

Gonzalo Tornar\'ia, Nathan C. Ryan

arxiv:1206.0072 v1 · 2012-06-01 · 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{S5CZUZ5XBRNQIR4P7RDL3DSYOG}

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	2026-05-18T03:54:27.161080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97459a67b70c5b04478ffc46bd8e5871a7a870b37f028040fa86f3f059ac353f

Aliases

arxiv: 1206.0072 · arxiv_version: 1206.0072v1 · doi: 10.48550/arxiv.1206.0072 · pith_short_12: S5CZUZ5XBRNQ · pith_short_16: S5CZUZ5XBRNQIR4P · pith_short_8: S5CZUZ5X

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/S5CZUZ5XBRNQIR4P7RDL3DSYOG \
  | 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: 97459a67b70c5b04478ffc46bd8e5871a7a870b37f028040fa86f3f059ac353f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b36f85ecba426351356feee59428414ee2f5bc398fb4a2c14c54a64d1070f833",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-01T03:39:12Z",
    "title_canon_sha256": "23c785717f0873fae46b139cb58c85cc0befd74bfa259b04c4ebc0da6eb08fda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0072",
    "kind": "arxiv",
    "version": 1
  }
}