Pith Number

pith:XHERDWKR

pith:2026:XHERDWKRPAIDCG7Q3S7XYA5ME4

not attested not anchored not stored refs pending

Faster Mixing for Triangulations via Transport Flows

Daniel Frishberg, Michail Sarantis, Prasad Tetali, Vedat Levi Alev

The triangulation flip chain on a convex (n+2)-gon mixes in Õ(n²) time.

arxiv:2605.02067 v2 · 2026-05-03 · math.CO · cs.CG · cs.DM · cs.DS

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\pithnumber{XHERDWKRPAIDCG7Q3S7XYA5ME4}

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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.

Claims

C1strongest claim

We prove an Õ(n²) bound for the relaxation time and the log-Sobolev time (inverse log-Sobolev constant) of the classical triangulation flip chain on a convex (n+2)-gon, implying a mixing time of Õ(n²).

C2weakest assumption

The analysis assumes that the transport flows framework from Chen et al. can be applied efficiently to combinatorial decompositions of the triangulation space without introducing hidden dependencies or loose constants that would invalidate the Õ(n²) bound.

C3one line summary

Proves Õ(n²) bound on relaxation and log-Sobolev times for the triangulation flip chain on convex polygons, improving the prior Õ(n³) upper bound.

Formal links

3 machine-checked theorem links

Cited by

2 papers in Pith

On weighted partial triangulations of convex polygons

Burnside process on parking functions and Dyck paths

Receipt and verification

First computed	2026-05-26T02:04:11.804911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9c911d9517810311bf0dcbf7c03ac2705006203affd153cb107055e01bdfbda

Aliases

arxiv: 2605.02067 · arxiv_version: 2605.02067v2 · doi: 10.48550/arxiv.2605.02067 · pith_short_12: XHERDWKRPAID · pith_short_16: XHERDWKRPAIDCG7Q · pith_short_8: XHERDWKR

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/XHERDWKRPAIDCG7Q3S7XYA5ME4 \
  | 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: b9c911d9517810311bf0dcbf7c03ac2705006203affd153cb107055e01bdfbda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69e286e97f88768d7af1ffc29de43d9512f7ebba2421e569da9483cd3c6b4232",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM",
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-03T21:44:00Z",
    "title_canon_sha256": "f931a3e4b9c5a46e20e1fa5caa83d1fb03bf3b35c458202569b5c0101c357546"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02067",
    "kind": "arxiv",
    "version": 2
  }
}