Pith Number

pith:B7Q2GIAS

pith:2026:B7Q2GIASMYKM2PM37GRDZIRHA4

not attested not anchored not stored refs pending

Stable complete coordinates for multisets of points via basic $r$-symmetric tropical polynomials

Susumu Kubo

arxiv:2606.30184 v1 · 2026-06-29 · cs.DM · math.AG · math.CO · math.MG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B7Q2GIASMYKM2PM37GRDZIRHA4}

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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

The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions

Receipt and verification

First computed	2026-06-30T02:17:52.882736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fe1a320126614cd3d9bf9a23ca2270701d3cc1613e7a0633fe395c133fef574

Aliases

arxiv: 2606.30184 · arxiv_version: 2606.30184v1 · doi: 10.48550/arxiv.2606.30184 · pith_short_12: B7Q2GIASMYKM · pith_short_16: B7Q2GIASMYKM2PM3 · pith_short_8: B7Q2GIAS

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/B7Q2GIASMYKM2PM37GRDZIRHA4 \
  | 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: 0fe1a320126614cd3d9bf9a23ca2270701d3cc1613e7a0633fe395c133fef574

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1c6d45174b8e003a21a9b5479fa4e7b6b40b73b0f8e46c55d51f11e799f22f8",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-06-29T11:58:08Z",
    "title_canon_sha256": "cc1b76cb9ead6923c4c94ff0a057cd285323177710c92c657a8973529d4a4e16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30184",
    "kind": "arxiv",
    "version": 1
  }
}