Pith Number

pith:TCHMOISM

pith:2014:TCHMOISMOB265XPJFFDFPD6TVQ

not attested not anchored not stored refs pending

New trigonometric identities and reciprocity laws of generalized Dedekind sums II

Genki Shibukawa

arxiv:1411.3321 v2 · 2014-10-18 · math.CA · 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{TCHMOISMOB265XPJFFDFPD6TVQ}

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	2026-05-18T01:36:20.327979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

988ec7224c7075eedde92946578fd3ac0993bfdf61a5cc21dc849de68ed18a8b

Aliases

arxiv: 1411.3321 · arxiv_version: 1411.3321v2 · doi: 10.48550/arxiv.1411.3321 · pith_short_12: TCHMOISMOB26 · pith_short_16: TCHMOISMOB265XPJ · pith_short_8: TCHMOISM

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/TCHMOISMOB265XPJFFDFPD6TVQ \
  | 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: 988ec7224c7075eedde92946578fd3ac0993bfdf61a5cc21dc849de68ed18a8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e44057a924f7b88f117f4e070653fa0877b6a36b33cf2d5efad336bdb16bad7d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-10-18T06:51:10Z",
    "title_canon_sha256": "77dbb0fbc3564b65171d82b4f8daf87e8681308b99a20b218d09e9f3005d5876"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.3321",
    "kind": "arxiv",
    "version": 2
  }
}