Pith Number

pith:XJRXHSWU

pith:2020:XJRXHSWUOYVIAYQRCZ5NNYEHUU

not attested not anchored not stored refs pending

The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron

Lauren K. Williams, Matteo Parisi, Tomasz Lukowski

arxiv:2002.06164 v4 · 2020-02-14 · math.CO · hep-th · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJRXHSWUOYVIAYQRCZ5NNYEHUU}

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

2 papers in Pith

Multi-Loop Negative Geometries

Noncrossing Duality and the Geometry of Positive Tropical Linear Spaces

Receipt and verification

First computed	2026-07-05T03:30:49.635290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba6373cad4762a806211167ad6e087a50b27b2676ed3ec8b7c4c3d6de9a83de9

Aliases

arxiv: 2002.06164 · arxiv_version: 2002.06164v4 · doi: 10.48550/arxiv.2002.06164 · pith_short_12: XJRXHSWUOYVI · pith_short_16: XJRXHSWUOYVIAYQR · pith_short_8: XJRXHSWU

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/XJRXHSWUOYVIAYQRCZ5NNYEHUU \
  | 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: ba6373cad4762a806211167ad6e087a50b27b2676ed3ec8b7c4c3d6de9a83de9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ea3b8ddbc10005bedc75f9b54ebabbf94d71a9d2f304f313fc765d8dfac12aa",
    "cross_cats_sorted": [
      "hep-th",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-02-14T18:30:49Z",
    "title_canon_sha256": "9623ed503418e83c6ab287051a63f7d5d1baaf5910221bcb2cc3a01481f48b37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.06164",
    "kind": "arxiv",
    "version": 4
  }
}