Pith Number

pith:3DAO54WO

pith:2026:3DAO54WOHSD6DXFWDXEDJGKWK7

not attested not anchored not stored refs resolved

Synchronization and metachronal waves in an array of eukaryotic flagella

Nariya Uchida, Yukinori Wakahara

Larger arrays of flagella sustain stable metachronal waves with fixed nonzero phase shifts between neighbors.

arxiv:2605.16705 v1 · 2026-05-15 · nlin.AO

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Record completeness

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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

larger arrays are found to support stable metachronal waves with finite phase differences. The analysis shows that increasing system size enlarges the set of stable phase-locked modes, thereby promoting metachronal-wave selection.

C2weakest assumption

The phase description for the array is constructed from the pair problem under the assumption of nearest-neighbor hydrodynamic coupling for the stability analysis of phase-locked states.

C3one line summary

Larger flagellar arrays stabilize metachronal waves through nearest-neighbor hydrodynamic coupling, as shown by phase stability analysis extending from pair problems and confirmed in direct numerical simulations.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] showsτ j(t)≈0, indicating in-phase synchronization. In Fig. 2(d), the steady state (t≳80) shows thatτ j(t) converges to a constant nonzero value, corresponding to a metachronal wave. In addition, stri

[2] S. L. Tamm, J. Cell Biol.55, 250 (1972) 1972

[3] D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Gold- stein, Phys. Rev. Lett.109, 268102 (2012) 2012

[4] M. A. Sleigh, J. R. Blake, and N. Liron, Am. Rev. Respir. Dis.137, 726 (1988) 1988

[5] J. E. P. Lever, K. B. Turner, C. M. Fernandez, H. M. Leung, S. S. Hussain, R.-J. Shei, V. Y. Lin, S. E. Birket, K. K. Chu, G. J. Tearney, and G. M. Solomon, Am. J. Physiol.-Lung Cell. Mol. Physiol.327 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:37.462223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8c0eef2ce3c87e1dcb61dc834995657f6af73a54c57b23f80f6c99e87083a3a

Aliases

arxiv: 2605.16705 · arxiv_version: 2605.16705v1 · doi: 10.48550/arxiv.2605.16705 · pith_short_12: 3DAO54WOHSD6 · pith_short_16: 3DAO54WOHSD6DXFW · pith_short_8: 3DAO54WO

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/3DAO54WOHSD6DXFWDXEDJGKWK7 \
  | 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: d8c0eef2ce3c87e1dcb61dc834995657f6af73a54c57b23f80f6c99e87083a3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d18625afbfa19fa199b9c9ec736baad5595cbfd71fc9ec1e3bac3f9405160cf3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.AO",
    "submitted_at": "2026-05-15T23:43:06Z",
    "title_canon_sha256": "bfa78509c7e186263b3a64f7f93690b9970e8d5c4dd9d5d511649288adf1b80c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16705",
    "kind": "arxiv",
    "version": 1
  }
}