Pith Number

pith:PZUAHXEK

pith:2017:PZUAHXEKDT5YVBGQ5OBOO25N3M

not attested not anchored not stored refs pending

The length classification of threefold flops via noncommutative algebras

Joseph Karmazyn

arxiv:1709.02720 v1 · 2017-09-08 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PZUAHXEKDT5YVBGQ5OBOO25N3M}

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	2026-05-18T00:35:44.929461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e6803dc8a1cfb8a84d0eb82e76baddb13ee40ac48446f843594d6786b595e3d

Aliases

arxiv: 1709.02720 · arxiv_version: 1709.02720v1 · doi: 10.48550/arxiv.1709.02720 · pith_short_12: PZUAHXEKDT5Y · pith_short_16: PZUAHXEKDT5YVBGQ · pith_short_8: PZUAHXEK

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/PZUAHXEKDT5YVBGQ5OBOO25N3M \
  | 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: 7e6803dc8a1cfb8a84d0eb82e76baddb13ee40ac48446f843594d6786b595e3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "174b0ebcb20ae486fe5c3167fcb8bc1e6793b7d264ec6562f61af5513a89505e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-09-08T14:34:13Z",
    "title_canon_sha256": "d23aaf186ded45853a7445fc49d2bf7d10d6938ee166257289e7f8b4e56a8c4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02720",
    "kind": "arxiv",
    "version": 1
  }
}