Pith Number

pith:R2YUCQ3Y

pith:2026:R2YUCQ3YGGMHPIT3W3KN7TMUWA

not attested not anchored not stored refs pending

On the adiabatic invariance of the action of a trapped wave

Ekaterina V. Shishkina, Serge N. Gavrilov

The adiabatic invariant of a trapped wave equals the ratio of its total energy to its frequency.

arxiv:2602.18815 v4 · 2026-02-21 · math-ph · math.MP · physics.class-ph

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\pithnumber{R2YUCQ3YGGMHPIT3W3KN7TMUWA}

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Record completeness

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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

defined in this manner, the adiabatic invariant can be calculated as the ratio of the total energy of the trapped wave to its frequency

C2weakest assumption

The total energy of the trapped wave is well-defined and unambiguous in the linear discrete-continuous system, despite the paper noting potential ambiguity in its definition; the prior 2024 result on history-independent amplitude is taken as given.

C3one line summary

The adiabatic invariant of a trapped wave is its total energy divided by frequency, generalizing the Hamiltonian case to discrete-continuous systems.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T02:05:41.249391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8eb1414378319877a27bb6d4dfcd94b024e98d5bc242d02390003c8ade2b50a5

Aliases

arxiv: 2602.18815 · arxiv_version: 2602.18815v4 · doi: 10.48550/arxiv.2602.18815 · pith_short_12: R2YUCQ3YGGMH · pith_short_16: R2YUCQ3YGGMHPIT3 · pith_short_8: R2YUCQ3Y

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/R2YUCQ3YGGMHPIT3W3KN7TMUWA \
  | 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: 8eb1414378319877a27bb6d4dfcd94b024e98d5bc242d02390003c8ade2b50a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49df312145db67eada0146c69f24258b4e446c4bb2ad2858254d16a1da2af6a6",
    "cross_cats_sorted": [
      "math.MP",
      "physics.class-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-02-21T12:19:46Z",
    "title_canon_sha256": "52ea21889301dbdb300f97798a65e2b1ab5fc5e73cd8a4d1f518d2f5db122160"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.18815",
    "kind": "arxiv",
    "version": 4
  }
}