Pith Number

pith:GPRZ6KPW

pith:2026:GPRZ6KPWPFDXVHSR2N3WM3STNU

not attested not anchored not stored refs resolved

Variational Openness

Francisco Monroy

Stationarity in open variational systems requires cancellation of the total first variation rather than separate bulk and boundary cancellations.

arxiv:2605.17032 v1 · 2026-05-16 · physics.class-ph · math-ph · math.MP

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Claims

C1strongest claim

Stationarity requires cancellation of the total first variation, not necessarily separate cancellation of bulk and boundary contributions. Separate Euler-Lagrange and boundary equations arise only when admissible variations are independently localizable.

C2weakest assumption

In regulated open systems, admissible variations form a graph subspace in which bulk and boundary displacements are linked by a compatibility operator, allowing nontrivial bulk-boundary action exchange before total cancellation occurs.

C3one line summary

Variational openness extends stationarity to open systems by distinguishing separable cases with independent variations from regulated cases using graph subspaces linked by compatibility operators.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Course of Theoretical Physics, vol 1976

[2] Prentice-Hall, Englewood Cliffs (1963) 1963

[3] Mir Pub- lishers, Moscow (1969) 1969

[4] Giaquinta, M., Hildebrandt, S.: Calculus of Variations I. Springer, Berlin (1996) 1996

[5] Springer, New York (2008) 2008

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:36.826301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33e39f29f679477a9e51d377666e536d27c5c68a3a38e2a864f1e40027f198e5

Aliases

arxiv: 2605.17032 · arxiv_version: 2605.17032v1 · doi: 10.48550/arxiv.2605.17032 · pith_short_12: GPRZ6KPWPFDX · pith_short_16: GPRZ6KPWPFDXVHSR · pith_short_8: GPRZ6KPW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GPRZ6KPWPFDXVHSR2N3WM3STNU \
  | 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: 33e39f29f679477a9e51d377666e536d27c5c68a3a38e2a864f1e40027f198e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97808d528ee7c3b9768a88d47a94cda0481d8d8815fe6950a5d2e52dbb21d758",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.class-ph",
    "submitted_at": "2026-05-16T15:00:49Z",
    "title_canon_sha256": "9dba7e5e84ab5d8fd78dc2a9be23c93a4223db2f3d116d8b070b084609193508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17032",
    "kind": "arxiv",
    "version": 1
  }
}