Pith Number

pith:XBUL7ZT3

pith:2004:XBUL7ZT37P7BMPP26TIIW33LIT

not attested not anchored not stored refs pending

Modular circle quotients and PL limit sets

Richard Evan Schwartz

arxiv:math/0401311 v1 · 2004-01-23 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBUL7ZT37P7BMPP26TIIW33LIT}

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	2026-05-18T02:38:00.185532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b868bfe67bfbfe163dfaf4d08b6f6b44f833673742c332d2b2cf355f04215f15

Aliases

arxiv: math/0401311 · arxiv_version: math/0401311v1 · doi: 10.48550/arxiv.math/0401311 · pith_short_12: XBUL7ZT37P7B · pith_short_16: XBUL7ZT37P7BMPP2 · pith_short_8: XBUL7ZT3

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/XBUL7ZT37P7BMPP26TIIW33LIT \
  | 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: b868bfe67bfbfe163dfaf4d08b6f6b44f833673742c332d2b2cf355f04215f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd6ff5d9823288203c57d2073af646c14e20e06ea2dc1ad7716f6f7ca0af03c3",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-01-23T12:29:31Z",
    "title_canon_sha256": "cc8809b32d0ae9b0ee152e1deb67dde4325906ddc739d841fbfaa48f12ebd299"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401311",
    "kind": "arxiv",
    "version": 1
  }
}