Pith Number

pith:FPHWREYO

pith:2026:FPHWREYOVOYLW6SLIQURQTHPGP

not attested not anchored not stored refs pending

Two aspects of graph 3-manifold groups

Hongbin Sun

arxiv:2607.04326 v1 · 2026-07-05 · 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{FPHWREYOVOYLW6SLIQURQTHPGP}

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	2026-07-07T02:19:08.956090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bcf68930eabb0bb7a4b4429184cef33db4bdf0989e66832b51cd00b63a43425

Aliases

arxiv: 2607.04326 · arxiv_version: 2607.04326v1 · doi: 10.48550/arxiv.2607.04326 · pith_short_12: FPHWREYOVOYL · pith_short_16: FPHWREYOVOYLW6SL · pith_short_8: FPHWREYO

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/FPHWREYOVOYLW6SLIQURQTHPGP \
  | 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: 2bcf68930eabb0bb7a4b4429184cef33db4bdf0989e66832b51cd00b63a43425

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c7fe99052ae666fb935c5d84d0457dfcad2fea33809fbeb66d367cc4041745e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-05T14:16:45Z",
    "title_canon_sha256": "3455373d3e6592286ca2d8621c4cb62c4d821b830aa3aa2d317ae91c9bd3d33c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04326",
    "kind": "arxiv",
    "version": 1
  }
}