Pith Number

pith:3IW7LCCF

pith:2018:3IW7LCCFY5PX2R5FKLABA7S3XY

not attested not anchored not stored refs pending

The logarithmic Picard group and its tropicalization

Jonathan Wise, Samouil Molcho

arxiv:1807.11364 v5 · 2018-07-30 · 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{3IW7LCCFY5PX2R5FKLABA7S3XY}

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

Universality for tropical and logarithmic maps

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

Receipt and verification

First computed	2026-07-05T04:05:55.249069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da2df58845c75f7d47a552c0107e5bbe00dc5ffd4a789c47875e42ef9218e33f

Aliases

arxiv: 1807.11364 · arxiv_version: 1807.11364v5 · doi: 10.48550/arxiv.1807.11364 · pith_short_12: 3IW7LCCFY5PX · pith_short_16: 3IW7LCCFY5PX2R5F · pith_short_8: 3IW7LCCF

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/3IW7LCCFY5PX2R5FKLABA7S3XY \
  | 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: da2df58845c75f7d47a552c0107e5bbe00dc5ffd4a789c47875e42ef9218e33f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd31441f81fca4d758267e624f6f83dfcf9422b2f84a929a3985596689d51ad0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-07-30T14:15:22Z",
    "title_canon_sha256": "607548d30ea8476585260ce545af0df15b83c6987fe3b0cbef747ea9f428c051"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.11364",
    "kind": "arxiv",
    "version": 5
  }
}