Pith Number

pith:5Q6VBGWB

pith:2018:5Q6VBGWBEXZ5QWQ3YLGXYYFTXE

not attested not anchored not stored refs pending

Modular cocycles and cup product

Roelof Bruggeman, YoungJu Choie

arxiv:1811.10359 v1 · 2018-11-26 · 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{5Q6VBGWBEXZ5QWQ3YLGXYYFTXE}

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	2026-05-17T23:59:56.682358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec3d509ac125f3d85a1bc2cd7c60b3b90ea113e3798ddd9ee08ad9595574ec21

Aliases

arxiv: 1811.10359 · arxiv_version: 1811.10359v1 · doi: 10.48550/arxiv.1811.10359 · pith_short_12: 5Q6VBGWBEXZ5 · pith_short_16: 5Q6VBGWBEXZ5QWQ3 · pith_short_8: 5Q6VBGWB

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/5Q6VBGWBEXZ5QWQ3YLGXYYFTXE \
  | 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: ec3d509ac125f3d85a1bc2cd7c60b3b90ea113e3798ddd9ee08ad9595574ec21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c6a8b7b25cd911f9b342299f593b303584d9ed270e7222e76b6aa20ef66786d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-26T13:29:31Z",
    "title_canon_sha256": "31dc08181c482469249c3fefd065016b64bcd595a71aabdd9f717bf51c4cf238"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.10359",
    "kind": "arxiv",
    "version": 1
  }
}