Pith Number

pith:2B3ROYMI

pith:2026:2B3ROYMISWQ5UXLD6UUMGFOU6J

not attested not anchored not stored refs pending

"True" self-avoiding walks on general trees

Tuan-Minh Nguyen

True self-avoiding walks on trees switch from recurrent to transient exactly when the branching-ruin number exceeds 1/2.

arxiv:2604.24389 v2 · 2026-04-27 · math.PR · cond-mat.stat-mech · math-ph · math.MP

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\usepackage{pith}
\pithnumber{2B3ROYMISWQ5UXLD6UUMGFOU6J}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 show that the process exhibits a sharp phase transition between recurrence and transience. The critical value is determined by the branching-ruin number of the tree. We prove that the walk is almost surely transient when the branching-ruin number is greater than 1/2, and recurrent when it is less than 1/2.

C2weakest assumption

The branching-ruin number of the tree equals the Hausdorff dimension of its boundary under a suitable metric, allowing the critical value to be located at 1/2.

C3one line summary

True self-avoiding walks on general trees are transient if the branching-ruin number exceeds 1/2 and recurrent otherwise.

Receipt and verification

First computed	2026-06-05T01:15:24.728121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d07717618895a1da5d63f528c315d4f247115291a1db0c6dc32b2bc06cb83990

Aliases

arxiv: 2604.24389 · arxiv_version: 2604.24389v2 · doi: 10.48550/arxiv.2604.24389 · pith_short_12: 2B3ROYMISWQ5 · pith_short_16: 2B3ROYMISWQ5UXLD · pith_short_8: 2B3ROYMI

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/2B3ROYMISWQ5UXLD6UUMGFOU6J \
  | 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: d07717618895a1da5d63f528c315d4f247115291a1db0c6dc32b2bc06cb83990

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f6e671b9046b07dcdcc4d239b9e568121d9fbd96c1212fe32c665f16486e158",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-27T12:18:08Z",
    "title_canon_sha256": "7e92e66c5212cb5493248cae718488d3dfb83a400df7472b8f535a5422cca0c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24389",
    "kind": "arxiv",
    "version": 2
  }
}