Pith Number

pith:BXUO6MIE

pith:2026:BXUO6MIENATQ3EY2HG2S26AYFR

not attested not anchored not stored refs pending

Sharp Phase Transition for the Formation of Infinite Tubes

Omer Bobrowski, Primoz Skraba, Shu Kanazawa

Tube percolation exhibits sharp thresholds at criticality for infinite tube formation, proven via OSSS inequality and adapted exploration algorithms.

arxiv:2605.14910 v1 · 2026-05-14 · math.PR

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\usepackage{pith}
\pithnumber{BXUO6MIENATQ3EY2HG2S26AYFR}

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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

the tubular one-arm event exhibits a sharp threshold at criticality: below criticality, its probability decays exponentially in scale, whereas above criticality, it admits a mean-field-type lower bound. [...] the existence of a box-crossing tube also exhibits a sharp threshold.

C2weakest assumption

The OSSS inequality applies to the Boolean function defined by the tubular one-arm event under the adapted exploration algorithm that respects tube topology, without hidden obstructions from non-transitivity of tube connectedness.

C3one line summary

Tube percolation exhibits sharp thresholds at criticality for infinite tube formation, proven via OSSS inequality and adapted exploration algorithms.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:55.768175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0de8ef310468270d931a39b52d78182c435accb989fc273a3f5b71cf65b9f748

Aliases

arxiv: 2605.14910 · arxiv_version: 2605.14910v1 · doi: 10.48550/arxiv.2605.14910 · pith_short_12: BXUO6MIENATQ · pith_short_16: BXUO6MIENATQ3EY2 · pith_short_8: BXUO6MIE

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/BXUO6MIENATQ3EY2HG2S26AYFR \
  | 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: 0de8ef310468270d931a39b52d78182c435accb989fc273a3f5b71cf65b9f748

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c47062605d8f8cf2d88acb8d3b6f754bb64a0da9ed2fc149f2cd98c4aeaa3608",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-14T14:44:28Z",
    "title_canon_sha256": "05c928f87f29a6e2d2c38097a6524fc7593caa9711c13fa91b2d418e74e5d490"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14910",
    "kind": "arxiv",
    "version": 1
  }
}