Pith Number

pith:ROCYJ6P4

pith:2017:ROCYJ6P4NOOKKV3KRLIVMXDQSK

not attested not anchored not stored refs pending

Picard groups for tropical toric schemes

Jaiung Jun, Jeffrey Tolliver, Kalina Mincheva

arxiv:1709.03130 v2 · 2017-09-10 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ROCYJ6P4NOOKKV3KRLIVMXDQSK}

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	2026-05-18T00:09:52.972664Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b8584f9fc6b9ca5576a8ad1565c70928880179c9ea131f99bdc7cd1c686deed

Aliases

arxiv: 1709.03130 · arxiv_version: 1709.03130v2 · doi: 10.48550/arxiv.1709.03130 · pith_short_12: ROCYJ6P4NOOK · pith_short_16: ROCYJ6P4NOOKKV3K · pith_short_8: ROCYJ6P4

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/ROCYJ6P4NOOKKV3KRLIVMXDQSK \
  | 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: 8b8584f9fc6b9ca5576a8ad1565c70928880179c9ea131f99bdc7cd1c686deed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d317a99d94d53b379193423b1fb2bf34778e7c33f5fc1e015393a2082ef5c0b9",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-09-10T16:43:07Z",
    "title_canon_sha256": "5dacd2b47e8f28ffa396d0d81f6874d94a50f664e72e4126e89a9defd105ab73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.03130",
    "kind": "arxiv",
    "version": 2
  }
}