Pith Number

pith:KOQDLMXC

pith:2026:KOQDLMXCNAZTYJ5YUSTC6Z7B4X

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Energy-Momentum Conservation as a Constraint to Restrict the Space of Viable Field Lagrangians: Vector Field versus Spin-Two Field

Antonio L\'opez-Pinto, Satoshi Nakajima

Conservation of the symmetrized Belinfante tensor for a symmetric tensor field coupled to matter is equivalent to Feynman's consistency condition and fixes the field Lagrangian to the Einstein form.

arxiv:2604.17601 v3 · 2026-04-19 · gr-qc · hep-th

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\usepackage{pith}
\pithnumber{KOQDLMXCNAZTYJ5YUSTC6Z7B4X}

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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

For a point particle coupled universally to the symmetric tensor field, we show that conservation of the total energy-momentum tensor is equivalent to Feynman's consistency condition. Assuming that the field Lagrangian is local, Lorentz invariant, and quadratic in first derivatives, this condition determines the Lagrangian, up to a total divergence, to be the Einstein Lagrangian density.

C2weakest assumption

The field Lagrangian is local, Lorentz invariant, and quadratic in first derivatives; the coupling of the symmetric tensor field to the point particle is universal.

C3one line summary

Conservation of the symmetrized Belinfante tensor is equivalent to Feynman's condition and determines the Einstein Lagrangian for a symmetric rank-two field on Minkowski space.

Receipt and verification

First computed	2026-05-25T02:01:20.666822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53a035b2e268333c27b8a4a62f67e1e5c92ddf7390d67334c32eb0204cf94701

Aliases

arxiv: 2604.17601 · arxiv_version: 2604.17601v3 · doi: 10.48550/arxiv.2604.17601 · pith_short_12: KOQDLMXCNAZT · pith_short_16: KOQDLMXCNAZTYJ5Y · pith_short_8: KOQDLMXC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KOQDLMXCNAZTYJ5YUSTC6Z7B4X \
  | 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: 53a035b2e268333c27b8a4a62f67e1e5c92ddf7390d67334c32eb0204cf94701

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4680aa2ab892fca2527ef62e2381f20d6cb9920daf3aa0659f686448d9dc9226",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-04-19T20:21:00Z",
    "title_canon_sha256": "0cd0c7bbace4b7998ea1de1aad05ae4de2ddb74ae26536f99f298a32f5734fa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17601",
    "kind": "arxiv",
    "version": 3
  }
}