Pith Number

pith:THR4LMTF

pith:2011:THR4LMTF2OIFHH6BI5HW6BI3GF

not attested not anchored not stored refs pending

Period functions and cotangent sums

Brian Conrey, Sandro Bettin

arxiv:1111.0931 v2 · 2011-11-03 · 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{THR4LMTF2OIFHH6BI5HW6BI3GF}

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	2026-05-18T01:10:55.063683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99e3c5b265d390539fc1474f6f051b314eb00b8f8589e55bfe3ef4f0b8be5758

Aliases

arxiv: 1111.0931 · arxiv_version: 1111.0931v2 · doi: 10.48550/arxiv.1111.0931 · pith_short_12: THR4LMTF2OIF · pith_short_16: THR4LMTF2OIFHH6B · pith_short_8: THR4LMTF

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/THR4LMTF2OIFHH6BI5HW6BI3GF \
  | 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: 99e3c5b265d390539fc1474f6f051b314eb00b8f8589e55bfe3ef4f0b8be5758

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6823d2a14825e3ef262b1932c307bade58608d79f9dcb546e17985548831840",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-03T17:54:46Z",
    "title_canon_sha256": "71a97bf2dfeec7bf22ef6dfeb326f71553092d3af7ba8d2be2ab1c7e459fc928"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0931",
    "kind": "arxiv",
    "version": 2
  }
}