Pith Number

pith:VLRJGZ2O

pith:2016:VLRJGZ2OCVEOYCXN3RNB5PFGAU

not attested not anchored not stored refs pending

The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity

Masaharu Ishikawa, Tat Thang Nguyen, Tien Son Pham

arxiv:1608.02679 v1 · 2016-08-09 · math.GT · 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{VLRJGZ2OCVEOYCXN3RNB5PFGAU}

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	2026-05-18T01:09:33.915803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aae293674e1548ec0aeddc5a1ebca6053373280c0e3ba8eac54930c87aea24f0

Aliases

arxiv: 1608.02679 · arxiv_version: 1608.02679v1 · doi: 10.48550/arxiv.1608.02679 · pith_short_12: VLRJGZ2OCVEO · pith_short_16: VLRJGZ2OCVEOYCXN · pith_short_8: VLRJGZ2O

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/VLRJGZ2OCVEOYCXN3RNB5PFGAU \
  | 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: aae293674e1548ec0aeddc5a1ebca6053373280c0e3ba8eac54930c87aea24f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "435da5636d323450f3cf59315124e1421717f29a1f1a34c35928b56ddde334ad",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-08-09T02:49:46Z",
    "title_canon_sha256": "92d8f3334c027affecfa3866341ef36ce701b04e7f5953d885f7ebaf3a0f7fb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02679",
    "kind": "arxiv",
    "version": 1
  }
}