Pith Number

pith:VKTJV65E

pith:2026:VKTJV65EWBHB4OWV4NXADGA3M5

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Entropic Collapse and Extreme First-Passage Times in Discrete Ballistic Transport

Bhargav R. Karamched

On hierarchical networks, minimum arrival times of many walkers follow a discrete distribution with a strict lower bound set by the graph, rather than any classical extreme-value law.

arxiv:2601.03622 v2 · 2026-01-07 · math-ph · math.MP

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Claims

C1strongest claim

the distribution of the minimum arrival time does not converge to any of the classical generalized extreme value distributions. Instead, it follows a discrete distribution with a strict lower time bound determined by the properties of the hierarchical network.

C2weakest assumption

The networks are discrete and hierarchical, walkers are non-interacting, and the transport regime can be cleanly classified as injection-limited versus bulk-limited so that the lower bound and entropic collapse apply as stated.

C3one line summary

In injection-limited hierarchical networks, minimum first-passage times of non-interacting walkers follow a discrete distribution with strict lower bound, destroyed by entropic collapse in bulk-limited geometries like the Bethe lattice.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Universality and ambiguity in extremes of anomalous diffusion

Receipt and verification

First computed	2026-05-17T23:39:00.304888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa69afba4b04e1e3ad5e36e01981b677060f0df4eaad293b97bbed0b5043ded

Aliases

arxiv: 2601.03622 · arxiv_version: 2601.03622v2 · doi: 10.48550/arxiv.2601.03622 · pith_short_12: VKTJV65EWBHB · pith_short_16: VKTJV65EWBHB4OWV · pith_short_8: VKTJV65E

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VKTJV65EWBHB4OWV4NXADGA3M5 \
  | 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: aaa69afba4b04e1e3ad5e36e01981b677060f0df4eaad293b97bbed0b5043ded

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea191e2e890381ae058bc44b036633d9f1d3d6d4b297c392f64609278efd7015",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-01-07T06:04:57Z",
    "title_canon_sha256": "045bfce070dbc5e3f312c56b0c86db730c00597511c7fb44ad85f6438a5fbfa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.03622",
    "kind": "arxiv",
    "version": 2
  }
}