Pith Number

pith:UGKJ46NY

pith:2016:UGKJ46NYDEWIBXH7NONLWMBZR7

not attested not anchored not stored refs pending

Generalized Tonnetze

Michael J. Catanzaro

arxiv:1612.03519 v1 · 2016-12-12 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UGKJ46NYDEWIBXH7NONLWMBZR7}

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	2026-05-17T23:56:58.914485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1949e79b8192c80dcff6b9abb30398fc4d88389feb219003bf1fd2609478ea2

Aliases

arxiv: 1612.03519 · arxiv_version: 1612.03519v1 · doi: 10.48550/arxiv.1612.03519 · pith_short_12: UGKJ46NYDEWI · pith_short_16: UGKJ46NYDEWIBXH7 · pith_short_8: UGKJ46NY

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/UGKJ46NYDEWIBXH7NONLWMBZR7 \
  | 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: a1949e79b8192c80dcff6b9abb30398fc4d88389feb219003bf1fd2609478ea2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba66bd0e7decba7b866560fd4a1d45066f3582328d9a66eb0bd0183365d8adb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-12-12T02:26:15Z",
    "title_canon_sha256": "51f30e83ba992ccf9d8d1d146626806af67c86cd8ec1614d814e732838eec2cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03519",
    "kind": "arxiv",
    "version": 1
  }
}