Pith Number

pith:BSJ7UVDK

pith:2026:BSJ7UVDKXDVTLBDGGC5FNX6CUG

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Elementary spectral invariants and three-dimensional Reeb dynamics

Michael Hutchings

Elementary spectral invariants of contact three-manifolds suffice to prove some results on the existence and properties of Reeb periodic orbits.

arxiv:2605.12958 v1 · 2026-05-13 · math.SG · math.DS

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Claims

C1strongest claim

Elementary spectral invariants of contact three-manifolds can be used to prove some results on the existence and properties of periodic orbits of Reeb vector fields, and they are a simplification of spectral invariants from embedded contact homology.

C2weakest assumption

That the elementary spectral invariants, defined by modifying alternative ECH capacities, retain enough information from the full ECH theory to support the claimed proofs for some results while being strictly simpler.

C3one line summary

Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.

References

75 extracted · 75 resolved · 0 Pith anchors

[1] C. Abbas, K. Cieliebak and H. Hofer,The Weinstein conjecture for planar contact structures in dimension three, Comm. Math. Helv.80(2005), 771–793 2005

[2] P. Albers, H. Geiges, and K. Zehmisch,Pseudorotations of the2-disc and Reeb flows on the3-sphere, Ergodic Theory Dynam. Systems,42(2022), 402–436 2022

[3] Bangert,On the existence of closed geodesics on two-spheres, Internat 1993

[4] Beiner,Infinite ECH capacities and Anosov flows, in preparation

[5] M. Borman, Y. Eliashberg, and E. Murphy,Existence and classification of overtwisted contact structures in all dimensions, Acta Math.215(2015), 281– 361 2015

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:09.238145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c93fa546ab8eb35846630ba56dfc2a193af8895375d49f7e727efbcdc437053

Aliases

arxiv: 2605.12958 · arxiv_version: 2605.12958v1 · doi: 10.48550/arxiv.2605.12958 · pith_short_12: BSJ7UVDKXDVT · pith_short_16: BSJ7UVDKXDVTLBDG · pith_short_8: BSJ7UVDK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BSJ7UVDKXDVTLBDGGC5FNX6CUG \
  | 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: 0c93fa546ab8eb35846630ba56dfc2a193af8895375d49f7e727efbcdc437053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc4f6427719e750d4d64af90a40d8929c48bb13fce8588b54d710b056cd21c03",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-05-13T03:43:20Z",
    "title_canon_sha256": "3a458b1383cc54e28ce52fc3b74706e2fd862ce24f154c9f1e155beb215eac3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12958",
    "kind": "arxiv",
    "version": 1
  }
}