Pith Number

pith:XBQ3JRMM

pith:2020:XBQ3JRMMTQ36ZDSGL34EY6UJ2P

not attested not anchored not stored refs pending

Theta-graph and diffeomorphisms of some 4-manifolds

Tadayuki Watanabe

arxiv:2005.09545 v4 · 2020-05-19 · 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{XBQ3JRMMTQ36ZDSGL34EY6UJ2P}

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.

Cited by

1 paper in Pith

Diffeomorphism groups and gauge theory for families

Receipt and verification

First computed	2026-07-05T05:44:45.733969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b861b4c58c9c37ec8e465ef84c7a89d3f6dafb5f1af13d7c526f8fef2840754d

Aliases

arxiv: 2005.09545 · arxiv_version: 2005.09545v4 · doi: 10.48550/arxiv.2005.09545 · pith_short_12: XBQ3JRMMTQ36 · pith_short_16: XBQ3JRMMTQ36ZDSG · pith_short_8: XBQ3JRMM

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/XBQ3JRMMTQ36ZDSGL34EY6UJ2P \
  | 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: b861b4c58c9c37ec8e465ef84c7a89d3f6dafb5f1af13d7c526f8fef2840754d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14ab586f03af73ee75646b4ef9059d27d56ef6bcad4b631b6b1c2b8aab69e426",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-05-19T16:00:30Z",
    "title_canon_sha256": "4846e73f9c493cc4e2a865b274f294c1c30725ced62c3bfb27c9b2c97cfe436d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2005.09545",
    "kind": "arxiv",
    "version": 4
  }
}