Pith Number

pith:Y2CA2D6K

pith:2012:Y2CA2D6KX72KEGEZ52G33EFGTL

not attested not anchored not stored refs pending

Singularities of Tangent Varieties to Curves and Surfaces

Goo Ishikawa

arxiv:1201.2778 v2 · 2012-01-13 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y2CA2D6KX72KEGEZ52G33EFGTL}

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	2026-05-18T04:02:14.670145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6840d0fcabff4a21899ee8dbd90a69ac7b4fad904647ce6eb4eb6566f12bf2d

Aliases

arxiv: 1201.2778 · arxiv_version: 1201.2778v2 · doi: 10.48550/arxiv.1201.2778 · pith_short_12: Y2CA2D6KX72K · pith_short_16: Y2CA2D6KX72KEGEZ · pith_short_8: Y2CA2D6K

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/Y2CA2D6KX72KEGEZ52G33EFGTL \
  | 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: c6840d0fcabff4a21899ee8dbd90a69ac7b4fad904647ce6eb4eb6566f12bf2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b39a92f975947c7035e9139cc918127217fa876a24a86c7f71c62f59aa3c40ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-13T09:27:20Z",
    "title_canon_sha256": "e9b4d017ced119a248fb76995c77b6ed57baff82d9ea7ed9e8b94422ea2bcc0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2778",
    "kind": "arxiv",
    "version": 2
  }
}