Pith Number

pith:BR4FENPT

pith:2014:BR4FENPTWSYPDC7ZFY4EU2WBKI

not attested not anchored not stored refs pending

Symmetric and r-Symmetric Tropical Polynomials and Rational Functions

Gunnar Carlsson, Sara Kalisnik Verovsek

arxiv:1405.2268 v5 · 2014-05-09 · 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{BR4FENPTWSYPDC7ZFY4EU2WBKI}

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

1 paper in Pith

Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry

Receipt and verification

First computed	2026-05-18T00:03:59.718749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c785235f3b4b0f18bf92e384a6ac152117dece8bb90f6f2872d4b57f46632d3

Aliases

arxiv: 1405.2268 · arxiv_version: 1405.2268v5 · doi: 10.48550/arxiv.1405.2268 · pith_short_12: BR4FENPTWSYP · pith_short_16: BR4FENPTWSYPDC7Z · pith_short_8: BR4FENPT

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/BR4FENPTWSYPDC7ZFY4EU2WBKI \
  | 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: 0c785235f3b4b0f18bf92e384a6ac152117dece8bb90f6f2872d4b57f46632d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fb1eb99bc756e34590bc9d7ea239c99ca1fc8d1484530104820c37e66262e29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2014-05-09T15:37:32Z",
    "title_canon_sha256": "1432f4e6d1315f9190732b4c0e7f37daa64b15d7baabb8ddd3d00a914ea6d0b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.2268",
    "kind": "arxiv",
    "version": 5
  }
}