Pith Number

pith:PKFANS6V

pith:2007:PKFANS6VHUEFF6JQI7BHK5USM6

not attested not anchored not stored refs pending

On tropical and Kapranov ranks of tropical matrices

Elena Rubei

arxiv:0712.3007 v3 · 2007-12-18 · 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{PKFANS6VHUEFF6JQI7BHK5USM6}

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	2026-05-18T04:22:32.060250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a8a06cbd53d0852f93047c275769267a80e28479aec8c8a813ab0ca3729e77f

Aliases

arxiv: 0712.3007 · arxiv_version: 0712.3007v3 · doi: 10.48550/arxiv.0712.3007 · pith_short_12: PKFANS6VHUEF · pith_short_16: PKFANS6VHUEFF6JQ · pith_short_8: PKFANS6V

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/PKFANS6VHUEFF6JQI7BHK5USM6 \
  | 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: 7a8a06cbd53d0852f93047c275769267a80e28479aec8c8a813ab0ca3729e77f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61d018194a2a4a1835a399c139ac0faf7e4b17dfa80e8c51e1be69c371dd44fd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-12-18T17:40:45Z",
    "title_canon_sha256": "f7112943f5a13b00bb8c49ce31164f0b9e231d5d6c8b6e376e5fb3229b94ce25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3007",
    "kind": "arxiv",
    "version": 3
  }
}