Pith Number

pith:KRLCFZZO

pith:2008:KRLCFZZOEUUCIP7XT22CYA3YWD

not attested not anchored not stored refs pending

Commensurability classes of (-2,3,n) pretzel knot complements

Melissa L. Macasieb, Thomas W. Mattman

arxiv:0804.0112 v1 · 2008-04-01 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRLCFZZOEUUCIP7XT22CYA3YWD}

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	2026-05-18T02:41:51.704426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

545622e72e2528243ff79eb42c0378b0c7341d6a16b921a8a4fe8e3261245a53

Aliases

arxiv: 0804.0112 · arxiv_version: 0804.0112v1 · doi: 10.48550/arxiv.0804.0112 · pith_short_12: KRLCFZZOEUUC · pith_short_16: KRLCFZZOEUUCIP7X · pith_short_8: KRLCFZZO

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/KRLCFZZOEUUCIP7XT22CYA3YWD \
  | 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: 545622e72e2528243ff79eb42c0378b0c7341d6a16b921a8a4fe8e3261245a53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a347d06eebe051cdf82ffee937084b73ee3811b4260e0e99404ebf032cfda95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-04-01T18:25:40Z",
    "title_canon_sha256": "a7b62c09ac7f8136e49b571af11ab93e3453260dff6668c8b2af1527aa185cac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.0112",
    "kind": "arxiv",
    "version": 1
  }
}