Pith Number

pith:UBLRJ5XQ

pith:2009:UBLRJ5XQGDY7SZWPMHPHXOVXV6

not attested not anchored not stored refs pending

Natural Commuting of Vanishing Cycles and the Verdier Dual

David B. Massey

arxiv:0908.2799 v1 · 2009-08-19 · 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{UBLRJ5XQGDY7SZWPMHPHXOVXV6}

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	2026-05-18T01:05:46.809789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a05714f6f030f1f966cf61de7bbab7af84c3ef004cfe52fb4f62f139d117b694

Aliases

arxiv: 0908.2799 · arxiv_version: 0908.2799v1 · doi: 10.48550/arxiv.0908.2799 · pith_short_12: UBLRJ5XQGDY7 · pith_short_16: UBLRJ5XQGDY7SZWP · pith_short_8: UBLRJ5XQ

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/UBLRJ5XQGDY7SZWPMHPHXOVXV6 \
  | 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: a05714f6f030f1f966cf61de7bbab7af84c3ef004cfe52fb4f62f139d117b694

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e375d695efc6e0975b0a2fa52024354917c7e605a440e9b6842c5e0b1e66d79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-08-19T19:27:03Z",
    "title_canon_sha256": "8fab0d2501175d111febb0088d1cf8021766a64f2abdc30ea1fee1ed9f78f7ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.2799",
    "kind": "arxiv",
    "version": 1
  }
}