Pith Number

pith:3B4AXXRX

pith:1999:3B4AXXRXMXJKHMZ6IG5SA4EW2I

not attested not anchored not stored refs pending

Exactness, integrality, and log modifications

Fumiharu Kato

arxiv:math/9907124 v2 · 1999-07-20 · 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{3B4AXXRXMXJKHMZ6IG5SA4EW2I}

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.

Cited by

1 paper in Pith

The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$

Receipt and verification

First computed	2026-07-05T02:09:27.712796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8780bde3765d2a3b33e41bb207096d2074818bda8b01d3ba726bdb6e22b5bb1

Aliases

arxiv: math/9907124 · arxiv_version: math/9907124v2 · doi: 10.48550/arxiv.math/9907124 · pith_short_12: 3B4AXXRXMXJK · pith_short_16: 3B4AXXRXMXJKHMZ6 · pith_short_8: 3B4AXXRX

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/3B4AXXRXMXJKHMZ6IG5SA4EW2I \
  | 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: d8780bde3765d2a3b33e41bb207096d2074818bda8b01d3ba726bdb6e22b5bb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b5c991c71512046cc9cd16ab272e52d6a6606ce2d7e6434b11fd7c503fd468b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-07-20T11:23:39Z",
    "title_canon_sha256": "d3239eb64658cc61a6dd1539a7447ee754a92c5114669ee536d42a534362d338"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907124",
    "kind": "arxiv",
    "version": 2
  }
}