Pith Number

pith:KNNM77LP

pith:2002:KNNM77LPHU4CPTSHR4FMOCTAS4

not attested not anchored not stored refs pending

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

Mihai Tibar

arxiv:math/0207108 v4 · 2002-07-12 · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KNNM77LPHU4CPTSHR4FMOCTAS4}

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	2026-05-18T01:19:55.988040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2

Aliases

arxiv: math/0207108 · arxiv_version: math/0207108v4 · doi: 10.48550/arxiv.math/0207108 · pith_short_12: KNNM77LPHU4C · pith_short_16: KNNM77LPHU4CPTSH · pith_short_8: KNNM77LP

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/KNNM77LPHU4CPTSHR4FMOCTAS4 \
  | 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: 535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb96b10c881d2e6c26bdb8104e7a326b7bedc1d7c22e293c05bcbf2385d44bff",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2002-07-12T14:44:12Z",
    "title_canon_sha256": "638da8f3fd160693fec7ff7adee48fa8879793a86083decabbe73cf8afd551b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0207108",
    "kind": "arxiv",
    "version": 4
  }
}