Pith Number

pith:FW5UCLMC

pith:2026:FW5UCLMCILZNQQRHRPLJKKUUFP

not attested not anchored not stored refs resolved

Branching under First-Passage Resetting

Aanjaneya Kumar, James Holehouse

Stochastic timing fluctuations in first-passage triggered replication enhance population growth for fixed offspring number and mean time.

arxiv:2605.16693 v1 · 2026-05-15 · q-bio.PE · cond-mat.stat-mech · math.PR · physics.bio-ph

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\pithnumber{FW5UCLMCILZNQQRHRPLJKKUUFP}

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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

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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

for fixed offspring number and fixed mean replication time, stochastic timing fluctuations necessarily enhance growth relative to a deterministic clock. When offspring yield depends on the first-passage time, fluctuations have non-trivial effects and expose a fundamental yield-delay trade-off.

C2weakest assumption

The population dynamics obey an exact renewal equation linking single-trajectory first-passage statistics to the population growth rate (abstract, paragraph 2), which presupposes that first-passage processes across independent lineages are statistically identical and that the branching occurs precisely at the first-passage event.

C3one line summary

New framework links first-passage timing statistics to branching population growth via renewal equations, showing fluctuations enhance growth for fixed offspring and mean time while exposing optimization trade-offs, with bacteriophage lysis application matching empirical data.

References

59 extracted · 59 resolved · 0 Pith anchors

[1] H. W. Watson and G. Galton, On the probability of the extinction of families, The Journal of the Anthropological Institute of Great Britain and Ireland4, 138 (1875)

[2] R. Bellman and T. E. Harris, On the theory of age- dependent stochastic branching processes, Proceedings of the National Academy of Sciences34, 601 (1948) 1948

[3] T. E. Harris, Branching processes, The Annals of Math- ematical Statistics , 474 (1948) 1948

[4] T. E. Harriset al.,The theory of branching processes, Vol. 6 (Springer Berlin, 1963) 1963

[5] S.AsmussenandH.Hering,Branchingprocesses, (1983) 1983

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:36.940046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dbb412d8242f2d842278bd6952a942bcd2cfb14d9fff5f116bed3cf0218c680

Aliases

arxiv: 2605.16693 · arxiv_version: 2605.16693v1 · doi: 10.48550/arxiv.2605.16693 · pith_short_12: FW5UCLMCILZN · pith_short_16: FW5UCLMCILZNQQRH · pith_short_8: FW5UCLMC

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/FW5UCLMCILZNQQRHRPLJKKUUFP \
  | 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: 2dbb412d8242f2d842278bd6952a942bcd2cfb14d9fff5f116bed3cf0218c680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "450fc7e282851f1f56bdb3ba66c8ffd1f9af2c9dae73b0c9422aa65aeef9a7ff",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.PR",
      "physics.bio-ph"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2026-05-15T23:10:35Z",
    "title_canon_sha256": "36ebeefc4498081ef050ad27cb840693f818383619e8886e9a1e7be504ffd7c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16693",
    "kind": "arxiv",
    "version": 1
  }
}