Pith Number

pith:X7IB6EK6

pith:2010:X7IB6EK6GNNOZQWATTK6HQJNRQ

not attested not anchored not stored refs pending

Tropical varieties with polynomial weights and corner loci of piecewise polynomials

Alexander Esterov

arxiv:1012.5800 v3 · 2010-12-28 · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X7IB6EK6GNNOZQWATTK6HQJNRQ}

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	2026-05-18T00:24:54.654463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfd01f115e335aecc2c09cd5e3c12d8c1162e3b0fba63925f4047ca08220071e

Aliases

arxiv: 1012.5800 · arxiv_version: 1012.5800v3 · doi: 10.48550/arxiv.1012.5800 · pith_short_12: X7IB6EK6GNNO · pith_short_16: X7IB6EK6GNNOZQWA · pith_short_8: X7IB6EK6

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/X7IB6EK6GNNOZQWATTK6HQJNRQ \
  | 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: bfd01f115e335aecc2c09cd5e3c12d8c1162e3b0fba63925f4047ca08220071e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6536475932ad0764c154c5c6461fd559518ae58e7d100481560b404f7fe386c9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-12-28T17:28:47Z",
    "title_canon_sha256": "0925f6b7328ce775ccb479f552ce3e6ac38d9aa32305301b5e5c3683335a32ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5800",
    "kind": "arxiv",
    "version": 3
  }
}