Pith Number

pith:FNJBCI5K

pith:2011:FNJBCI5KRIOELC36JRFNRK4TGV

not attested not anchored not stored refs pending

On tropical dualities in cluster algebras

Andrei Zelevinsky, Tomoki Nakanishi

arxiv:1101.3736 v3 · 2011-01-19 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNJBCI5KRIOELC36JRFNRK4TGV}

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	2026-05-18T04:00:13.708964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b521123aa8a1c458b7e4c4ad8ab93356becc72d40c1f3c3fb2d3f0cd368180a

Aliases

arxiv: 1101.3736 · arxiv_version: 1101.3736v3 · doi: 10.48550/arxiv.1101.3736 · pith_short_12: FNJBCI5KRIOE · pith_short_16: FNJBCI5KRIOELC36 · pith_short_8: FNJBCI5K

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/FNJBCI5KRIOELC36JRFNRK4TGV \
  | 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: 2b521123aa8a1c458b7e4c4ad8ab93356becc72d40c1f3c3fb2d3f0cd368180a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "927bdf4dfc1727db06044f3880c25a05dbd5bcbed3dc45b1b6d0270d1a939c90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-01-19T16:46:21Z",
    "title_canon_sha256": "221f0affdd04fed2e9bee4109daf1fef92c0f3efebe22cd4a487b2d0aa4146a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3736",
    "kind": "arxiv",
    "version": 3
  }
}