Pith Number

pith:TPTSCHB5

pith:2016:TPTSCHB5IMRQ32EJOUIVPXAA4R

not attested not anchored not stored refs pending

Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds II. Invariants of 3-manifolds with $b_1=1$

Tadayuki Watanabe

arxiv:1605.05620 v4 · 2016-05-18 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPTSCHB5IMRQ32EJOUIVPXAA4R}

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	2026-05-18T00:44:58.044234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be7211c3d43230de889751157dc00e4775472e3c6d78c58057c94afe082ff9a

Aliases

arxiv: 1605.05620 · arxiv_version: 1605.05620v4 · doi: 10.48550/arxiv.1605.05620 · pith_short_12: TPTSCHB5IMRQ · pith_short_16: TPTSCHB5IMRQ32EJ · pith_short_8: TPTSCHB5

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/TPTSCHB5IMRQ32EJOUIVPXAA4R \
  | 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: 9be7211c3d43230de889751157dc00e4775472e3c6d78c58057c94afe082ff9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36a329ed15b887805c044673048427e14e6da74ab1590a4f7346fa8fa48b8e21",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-05-18T15:35:18Z",
    "title_canon_sha256": "069e7c063a46085403fc6ef8e0bbe04f0d1bfdd7e53b29c19e7e1d48293a485a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05620",
    "kind": "arxiv",
    "version": 4
  }
}