Pith Number

pith:QTKA7NA6

pith:2024:QTKA7NA662X7D5I2J5TZHM4OSQ

not attested not anchored not stored refs pending

Essential tori in 3-manifolds not detected in any characteristic

Benjamin Martin, Grace S. Garden, Stephan Tillmann

arxiv:2411.15680 v1 · 2024-11-24 · 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{QTKA7NA662X7D5I2J5TZHM4OSQ}

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	2026-07-05T09:39:39.226240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84d40fb41ef6aff1f51a4f6793b38e94043ff2522a6fc62f6ae0c020f55fb934

Aliases

arxiv: 2411.15680 · arxiv_version: 2411.15680v1 · doi: 10.48550/arxiv.2411.15680 · pith_short_12: QTKA7NA662X7 · pith_short_16: QTKA7NA662X7D5I2 · pith_short_8: QTKA7NA6

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/QTKA7NA662X7D5I2J5TZHM4OSQ \
  | 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: 84d40fb41ef6aff1f51a4f6793b38e94043ff2522a6fc62f6ae0c020f55fb934

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c6d046c82e9cc79692bd20dbeeb194a95c63c1f242b966a9b70832450006cbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-11-24T01:31:55Z",
    "title_canon_sha256": "ee8d32379a31c5df294be2cee144449292516365fc5c13db91abd3579abcef18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.15680",
    "kind": "arxiv",
    "version": 1
  }
}