Pith Number

pith:TQGRCTGT

pith:2026:TQGRCTGTEBB44TOJT3L3PCEY5V

not attested not anchored not stored refs pending

Hyperbolic manifolds without positive spun triangulations

David Futer, Jessica S. Purcell, Saul Schleimer

arxiv:2607.08473 v1 · 2026-07-09 · 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{TQGRCTGTEBB44TOJT3L3PCEY5V}

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	2026-07-10T01:19:51.542723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c0d114cd32043ce4dc99ed7b78898ed5ac44c549e987cd0e33ef24265660852

Aliases

arxiv: 2607.08473 · arxiv_version: 2607.08473v1 · doi: 10.48550/arxiv.2607.08473 · pith_short_12: TQGRCTGTEBB4 · pith_short_16: TQGRCTGTEBB44TOJ · pith_short_8: TQGRCTGT

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/TQGRCTGTEBB44TOJT3L3PCEY5V \
  | 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: 9c0d114cd32043ce4dc99ed7b78898ed5ac44c549e987cd0e33ef24265660852

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6ab3cf21888099dad54f2ce1ed3277ba710712cc38008b8418fda0462330a72",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-09T13:30:04Z",
    "title_canon_sha256": "bf4a20d160953e37fd7517236600e3b824441690e9258eda45061023329cd65c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08473",
    "kind": "arxiv",
    "version": 1
  }
}