Pith Number

pith:TNC3GAMP

pith:2018:TNC3GAMPQGGTBN7QAPEYUX4IA7

not attested not anchored not stored refs pending

Geometry and algorithms for upper triangular tropical matrix identities

Marianne Johnson, Ngoc Mai Tran

arxiv:1806.01835 v2 · 2018-06-05 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TNC3GAMPQGGTBN7QAPEYUX4IA7}

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	2026-05-18T00:08:20.604122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b45b3018f818d30b7f003c98a5f8807c25b8a22e9f07c01bd81de42bee08109

Aliases

arxiv: 1806.01835 · arxiv_version: 1806.01835v2 · doi: 10.48550/arxiv.1806.01835 · pith_short_12: TNC3GAMPQGGT · pith_short_16: TNC3GAMPQGGTBN7Q · pith_short_8: TNC3GAMP

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/TNC3GAMPQGGTBN7QAPEYUX4IA7 \
  | 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: 9b45b3018f818d30b7f003c98a5f8807c25b8a22e9f07c01bd81de42bee08109

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b086890b1ca616515f8728914808b07a77bfdd890c80e4c469b6f9280044f215",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-05T17:42:35Z",
    "title_canon_sha256": "3f79df9daab2910ad3c693dfb633f9eab2f9d57961fc7799a3e614fca9b33d4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.01835",
    "kind": "arxiv",
    "version": 2
  }
}