Pith Number

pith:U4IBX7QF

pith:2026:U4IBX7QFGMYEPTVBNNWDWJVEPU

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Two-dimensional FrBD friction models for rolling contact

Luigi Romano

A two-dimensional FrBD model for rolling contact eliminates sliding velocity via the Implicit Function Theorem and preserves passivity in its linear formulations for nearly all practical parameters.

arxiv:2601.06811 v10 · 2026-01-11 · physics.app-ph

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4 Citations 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 the linear formulations, the analysis reveals that the model preserves passivity under almost any parametrisation of practical interest.

C2weakest assumption

The derivation relies on the Implicit Function Theorem being applicable to eliminate sliding velocity, which requires the local sliding-friction law to satisfy suitable invertibility conditions that are not verified in the abstract.

C3one line summary

A two-dimensional dynamic friction model for rolling contact is obtained by generalizing the FrBD framework, combining a rheological bristle representation with an analytical sliding law, and using the Implicit Function Theorem to eliminate sliding velocity.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T02:04:49.894778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7101bfe05333047cea16b6c3b26a47d1686569832e924ca92e258d29eab8731

Aliases

arxiv: 2601.06811 · arxiv_version: 2601.06811v10 · doi: 10.48550/arxiv.2601.06811 · pith_short_12: U4IBX7QFGMYE · pith_short_16: U4IBX7QFGMYEPTVB · pith_short_8: U4IBX7QF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U4IBX7QFGMYEPTVBNNWDWJVEPU \
  | 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: a7101bfe05333047cea16b6c3b26a47d1686569832e924ca92e258d29eab8731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c70f19066ea9fa9891b065b6366085204dd88c7caeb628a2e2c4b4e07a216b17",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.app-ph",
    "submitted_at": "2026-01-11T08:50:45Z",
    "title_canon_sha256": "684cc7755fcab7c5ec5a14c7fae81a9dc9920843f031c04d9c525b46f73b8b10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.06811",
    "kind": "arxiv",
    "version": 10
  }
}