Pith Number

pith:TWK5USYH

pith:2016:TWK5USYHJEM3J435IALT4FLEMP

not attested not anchored not stored refs pending

Shadows of 4-manifolds with complexity zero and polyhedral collapsing

Hironobu Naoe

arxiv:1605.00250 v2 · 2016-05-01 · 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{TWK5USYHJEM3J435IALT4FLEMP}

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	2026-05-18T00:52:23.390292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d95da4b074919b4f37d40173e156463f0cb7c1395247418c5dfd99dd1becf6e

Aliases

arxiv: 1605.00250 · arxiv_version: 1605.00250v2 · doi: 10.48550/arxiv.1605.00250 · pith_short_12: TWK5USYHJEM3 · pith_short_16: TWK5USYHJEM3J435 · pith_short_8: TWK5USYH

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/TWK5USYHJEM3J435IALT4FLEMP \
  | 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: 9d95da4b074919b4f37d40173e156463f0cb7c1395247418c5dfd99dd1becf6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b5175fd1696f8b16f5979d87f4d91d67a2584fd967e7ab3cb9407bfa4050aec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-05-01T13:16:43Z",
    "title_canon_sha256": "31026e75a3dd7f9de696a0648fee0e50f091a30553897a9f13859af6db8eb6b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00250",
    "kind": "arxiv",
    "version": 2
  }
}