Pith Number

pith:GXV3QNV6

pith:2026:GXV3QNV66J6GHMVV6NGZCY55XD

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Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori

Bassam Fayad, Dmitry Dolgopyat, Jaime Paradela

An abstract KAM theorem constructs full-dimensional tori in infinite particle systems with long-range interactions.

arxiv:2605.15928 v1 · 2026-05-15 · math.DS

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Record completeness

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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

Using this framework, we construct full-dimensional KAM tori for infinite-dimensional mechanical systems exhibiting long range interactions.

C2weakest assumption

The particle masses decay sufficiently fast and the interactions are all-to-all with suitable decay, allowing the abstract KAM theorem to apply to the infinite-dimensional mechanical system.

C3one line summary

An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.

References

130 extracted · 130 resolved · 1 Pith anchors

[1] Corsi, L. and Gentile, G. and Procesi, M. , TITLE =. Regul. Chaotic Dyn. , FJOURNAL =. 2024 , NUMBER =. doi:10.1134/S1560354724540025 , URL = 2024 · doi:10.1134/s1560354724540025

[2] Lindenstrauss, Joram , TITLE =. Israel J. Math. , FJOURNAL =. 1967 , PAGES =. doi:10.1007/BF02771101 , URL = 1967 · doi:10.1007/bf02771101

[3] Biasco, Luca and Chierchia, Luigi and Valdinoci, Enrico , TITLE =. SIAM J. Math. Anal. , FJOURNAL =. 2006 , NUMBER =. doi:10.1137/S0036141004443646 , URL = 2006 · doi:10.1137/s0036141004443646

[4] Mujica, J. , TITLE =. 1986 , PAGES = 1986

[5] Springer, New York, NY , 3 edition 1995 · doi:10.1007/978-1-4612-4182-9

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:45.478516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35ebb836bef27c63b2b5f34d9163bdb8fb7b7656ed42ddb1b5df3d2c633c0442

Aliases

arxiv: 2605.15928 · arxiv_version: 2605.15928v1 · doi: 10.48550/arxiv.2605.15928 · pith_short_12: GXV3QNV66J6G · pith_short_16: GXV3QNV66J6GHMVV · pith_short_8: GXV3QNV6

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/GXV3QNV66J6GHMVV6NGZCY55XD \
  | 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: 35ebb836bef27c63b2b5f34d9163bdb8fb7b7656ed42ddb1b5df3d2c633c0442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfc70bd97d8f50074909affae51d2a9cceae86ddb84a5ab159aaaae1c4a3ef9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T13:11:56Z",
    "title_canon_sha256": "687363316f40d78b75440595ea29977971f31ddc371d2e28a3dde5966a3017db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15928",
    "kind": "arxiv",
    "version": 1
  }
}