Pith Number

pith:WBUYBSJW

pith:2025:WBUYBSJWSDFQWUKFZQQJAFYWDQ

not attested not anchored not stored refs pending

Resident fitness computation in linear time and other algorithmic aspects of interacting trajectories

Andr\'as T\'obi\'as, Katalin Friedl, Vikt\'oria Nemkin

Resident fitness for n interacting trajectories is computable in O(n) time.

arxiv:2502.11561 v4 · 2025-02-17 · cs.DS · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WBUYBSJWSDFQWUKFZQQJAFYWDQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

Although the interaction of n trajectories may yield Ω(n²) slope changes in total, the resident fitness function can be computed algorithmically in O(n) time.

C2weakest assumption

The system consists of [0,1]-valued piecewise linear trajectories whose interactions are captured by the continued lines representation, and resident fitness is defined precisely as the cumulative sum of ultimate slopes of trajectories reaching height 1; this representation must allow direct computation without enumerating all slope changes.

C3one line summary

Resident fitness in systems of n interacting [0,1]-valued piecewise linear trajectories can be computed in O(n) time.

Cited by

1 paper in Pith

Resident fitness computation in linear time and other algorithmic aspects of interacting trajectories

Receipt and verification

First computed	2026-06-10T01:09:15.581181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b06980c93690cb0b5145cc209017161c15daec83499850dae56679b085498d6b

Aliases

arxiv: 2502.11561 · arxiv_version: 2502.11561v4 · doi: 10.48550/arxiv.2502.11561 · pith_short_12: WBUYBSJWSDFQ · pith_short_16: WBUYBSJWSDFQWUKF · pith_short_8: WBUYBSJW

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/WBUYBSJWSDFQWUKFZQQJAFYWDQ \
  | 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: b06980c93690cb0b5145cc209017161c15daec83499850dae56679b085498d6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e6ed5d4f32f39b4a86d0944af6564cf1a2f33e541a1d02f5ce4f0f8d9dd1a17",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2025-02-17T08:48:29Z",
    "title_canon_sha256": "06acc37a7ea921241309a42606065b7345ecfbe16eab06d31f9216a8b3b7e009"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.11561",
    "kind": "arxiv",
    "version": 4
  }
}