Pith Number

pith:7QAGDLL3

pith:2025:7QAGDLL3TSGQWIGHDE7734UYC6

not attested not anchored not stored refs pending

$\pi_1$-injective bounding and application to 3- and 4-manifolds

Jianfeng Lin, Zhongzi Wang

arxiv:2506.08847 v2 · 2025-06-10 · 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{7QAGDLL3TSGQWIGHDE7734UYC6}

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	2026-07-05T11:19:53.994179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc0061ad7b9c8d0b20c7193ffdf29817b0d238ba5d06f2d1cad4758734b50fbb

Aliases

arxiv: 2506.08847 · arxiv_version: 2506.08847v2 · doi: 10.48550/arxiv.2506.08847 · pith_short_12: 7QAGDLL3TSGQ · pith_short_16: 7QAGDLL3TSGQWIGH · pith_short_8: 7QAGDLL3

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/7QAGDLL3TSGQWIGHDE7734UYC6 \
  | 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: fc0061ad7b9c8d0b20c7193ffdf29817b0d238ba5d06f2d1cad4758734b50fbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdc2c22c47cff2f576c62a54d28e617a93f2180f1ed7f44241224e6a07cec585",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-06-10T14:35:46Z",
    "title_canon_sha256": "dc0abd9370714eb82f0772edf89944315984ea5a476088f90d3aeff05e9ee3bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08847",
    "kind": "arxiv",
    "version": 2
  }
}