Pith Number

pith:CK2MTYFG

pith:2012:CK2MTYFG6M4QGKS32RPB7NW5KT

not attested not anchored not stored refs pending

Reaching generalized critical values of a polynomial

Krzysztof Kurdyka, Zbigniew Jelonek

arxiv:1203.0539 v2 · 2012-03-02 · 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{CK2MTYFG6M4QGKS32RPB7NW5KT}

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	2026-05-18T01:19:22.555259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b4c9e0a6f339032a5bd45e1fb6dd54f718c8dd1b62e5fb15f21b2b3ef1cf76

Aliases

arxiv: 1203.0539 · arxiv_version: 1203.0539v2 · doi: 10.48550/arxiv.1203.0539 · pith_short_12: CK2MTYFG6M4Q · pith_short_16: CK2MTYFG6M4QGKS3 · pith_short_8: CK2MTYFG

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/CK2MTYFG6M4QGKS32RPB7NW5KT \
  | 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: 12b4c9e0a6f339032a5bd45e1fb6dd54f718c8dd1b62e5fb15f21b2b3ef1cf76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee22a94f2e40f5466e3b38db45c5c4d09fea6c733f32bd310f0047b2490ebe98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-03-02T18:05:31Z",
    "title_canon_sha256": "09e11e6af05fb6be2ca7a0b7504b2ccef5a45c74aa9853dbb70d4d6ecdeba6ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0539",
    "kind": "arxiv",
    "version": 2
  }
}