Pith Number

pith:VC5DKVKX

pith:2019:VC5DKVKXQMPLZSFDPPTVNC4LOW

not attested not anchored not stored refs pending

A note on the cycle of curves in a product of pairs

Dhruv Ranganathan

arxiv:1910.00239 v2 · 2019-10-01 · 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{VC5DKVKXQMPLZSFDPPTVNC4LOW}

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

2 papers in Pith

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

Receipt and verification

First computed	2026-07-05T04:58:13.511352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8ba355557831ebcc8a37be7568b8b7596008bdb9a460a86cbfe732b97e7dcaa

Aliases

arxiv: 1910.00239 · arxiv_version: 1910.00239v2 · doi: 10.48550/arxiv.1910.00239 · pith_short_12: VC5DKVKXQMPL · pith_short_16: VC5DKVKXQMPLZSFD · pith_short_8: VC5DKVKX

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/VC5DKVKXQMPLZSFDPPTVNC4LOW \
  | 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: a8ba355557831ebcc8a37be7568b8b7596008bdb9a460a86cbfe732b97e7dcaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cc757e31989ebe6b427db6ae61d0d16194b0c8a1ab12a699c08a66af4d5a2a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-10-01T08:02:44Z",
    "title_canon_sha256": "256ae5472e7613df4265ec8680f9b76449b47d0f9cd6ce5b7897980c03ea2896"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.00239",
    "kind": "arxiv",
    "version": 2
  }
}