Pith Number

pith:KBBDBYOI

pith:2013:KBBDBYOIJSUNDPKGPIRMAUCQAK

not attested not anchored not stored refs pending

Fourier-Dedekind Sums and an Extension of Rademacher Reciprocity

Emmanuel Tsukerman

arxiv:1307.5542 v4 · 2013-07-21 · math.NT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KBBDBYOIJSUNDPKGPIRMAUCQAK}

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	2026-05-18T03:11:23.751689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

504230e1c84ca8d1bd467a22c050500292ac1ebc9b5543451c684d664799439c

Aliases

arxiv: 1307.5542 · arxiv_version: 1307.5542v4 · doi: 10.48550/arxiv.1307.5542 · pith_short_12: KBBDBYOIJSUN · pith_short_16: KBBDBYOIJSUNDPKG · pith_short_8: KBBDBYOI

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/KBBDBYOIJSUNDPKGPIRMAUCQAK \
  | 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: 504230e1c84ca8d1bd467a22c050500292ac1ebc9b5543451c684d664799439c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9997abd3bbf678c45ce5179879fba35b3dddb80b18b114e87312117a519dd5ba",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-21T16:51:27Z",
    "title_canon_sha256": "d3448684810748f7f15a896ed04d91f3cfcd0da5ab0e39ffca9a088bc97a627d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5542",
    "kind": "arxiv",
    "version": 4
  }
}