Pith Number

pith:7QZDCNWC

pith:2017:7QZDCNWCC2O55VUHPMNEUCPZQO

not attested not anchored not stored refs pending

Upper bounds on Betti numbers of tropical prevarieties

Dima Grigoriev, Nicolai Vorobjov

arxiv:1709.08594 v2 · 2017-09-25 · 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{7QZDCNWCC2O55VUHPMNEUCPZQO}

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	2026-05-18T00:21:38.710799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605

Aliases

arxiv: 1709.08594 · arxiv_version: 1709.08594v2 · doi: 10.48550/arxiv.1709.08594 · pith_short_12: 7QZDCNWCC2O5 · pith_short_16: 7QZDCNWCC2O55VUH · pith_short_8: 7QZDCNWC

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/7QZDCNWCC2O55VUHPMNEUCPZQO \
  | 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: fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e942f384bae6edbe45c79882dba034d9bc69cfc677dc050887255e4da4dc031",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-09-25T16:51:21Z",
    "title_canon_sha256": "f334fdfe1fbd159b72aec70b2a6ef040ceb9a56bb29fe2db4cd968cbe6b49d25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.08594",
    "kind": "arxiv",
    "version": 2
  }
}