Pith Number

pith:OCXE2HAE

pith:2010:OCXE2HAELSLILHF44E6Q6DTTRH

not attested not anchored not stored refs pending

Morse theory and toric vector bundles

David Treumann

arxiv:1010.4071 v2 · 2010-10-19 · 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{OCXE2HAELSLILHF44E6Q6DTTRH}

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	2026-05-18T04:24:36.185283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70ae4d1c045c96859cbce13d0f0e7389e78bb7fff6a8a5a369f272e2ddfe6c33

Aliases

arxiv: 1010.4071 · arxiv_version: 1010.4071v2 · doi: 10.48550/arxiv.1010.4071 · pith_short_12: OCXE2HAELSLI · pith_short_16: OCXE2HAELSLILHF4 · pith_short_8: OCXE2HAE

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/OCXE2HAELSLILHF44E6Q6DTTRH \
  | 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: 70ae4d1c045c96859cbce13d0f0e7389e78bb7fff6a8a5a369f272e2ddfe6c33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb2bada7063bac06d49a139856de5e77afed325531b3151cf0a342066ac504b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-19T23:08:34Z",
    "title_canon_sha256": "f7bcd9de1f02aff2489d1012e7dc707c61cf20b67394c9bdf6b7d3b5fbbfc17c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4071",
    "kind": "arxiv",
    "version": 2
  }
}