{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PCJYS4YJBFMNTSPHUEAKMCF3ES","short_pith_number":"pith:PCJYS4YJ","canonical_record":{"source":{"id":"2604.09500","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-04-10T17:13:22Z","cross_cats_sorted":[],"title_canon_sha256":"acb79d41c925f4aa958a78834d16673acb9d344ffd12c6ae9c53f5c9e6e24b5e","abstract_canon_sha256":"477f081811551ef2b1aa84a4e82ce2484c4b4226a15c928c0fc44a3148cb9598"},"schema_version":"1.0"},"canonical_sha256":"78938973090958d9c9e7a100a608bb24a039d23bfe3caca4922356665625bfa5","source":{"kind":"arxiv","id":"2604.09500","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.09500","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"2604.09500v2","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.09500","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"PCJYS4YJBFMN","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_16","alias_value":"PCJYS4YJBFMNTSPH","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_8","alias_value":"PCJYS4YJ","created_at":"2026-07-20T00:18:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PCJYS4YJBFMNTSPHUEAKMCF3ES","target":"record","payload":{"canonical_record":{"source":{"id":"2604.09500","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-04-10T17:13:22Z","cross_cats_sorted":[],"title_canon_sha256":"acb79d41c925f4aa958a78834d16673acb9d344ffd12c6ae9c53f5c9e6e24b5e","abstract_canon_sha256":"477f081811551ef2b1aa84a4e82ce2484c4b4226a15c928c0fc44a3148cb9598"},"schema_version":"1.0"},"canonical_sha256":"78938973090958d9c9e7a100a608bb24a039d23bfe3caca4922356665625bfa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T00:18:20.514493Z","signature_b64":"2Hoer6/xk01f2RRtcwJl1WeEiHezPJg1eVNzPFkhx9fPWGcnDW5KB7aDsY9OVI4jfeniYAlfjnN5+N6rNicMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78938973090958d9c9e7a100a608bb24a039d23bfe3caca4922356665625bfa5","last_reissued_at":"2026-07-20T00:18:20.513483Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T00:18:20.513483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.09500","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-20T00:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AHoUnTN0dpS9OSmiwZMnrPM1c7gacULq+WfedwOX19y1VyJEAYlB381XnXxtC8LDG5UdMhj6sU9tNOgcePaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:32:04.239424Z"},"content_sha256":"a34b0161c049a96bc7044f819c7086877479c2af27d48d7ebb4c682332cb2f6c","schema_version":"1.0","event_id":"sha256:a34b0161c049a96bc7044f819c7086877479c2af27d48d7ebb4c682332cb2f6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PCJYS4YJBFMNTSPHUEAKMCF3ES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conservation laws in classical Poisson field theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case.","cross_cats":[],"primary_cat":"hep-th","authors_text":"M. J. Neves, O. Abla","submitted_at":"2026-04-10T17:13:22Z","abstract_excerpt":"Poisson electrodynamics is the semiclassical limit of the full $U(1)$ non-commutative gauge theory, also known in recent literature as Poisson gauge theory. Two consolidated models for the theory studied in recent years, with a specific choice of non-commutative parameter, Lie-Poisson structures and constant ones, the later also known as the canonical, or Heisenberg case. In this paper, we present the theory considering the new building blocks related to symmetries and conservation laws, as a first step toward understanding the necessary mathematical tools to uncover some of the unknown pieces"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the non-relativistic limit for the κ-Minkowski Dirac equation, the energy shift in the first excited state depends exclusively on the κ-parameter, and the non-relativistic limit introduces an orbital Zeeman coupling term for the fermionic fields.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The recently developed action principle for Lie-Poisson electrodynamics can be directly applied to derive conservation laws for the scalar and Dirac fields without introducing inconsistencies in the κ-Minkowski framework.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8d5c402f1b3471d800ddd397188a45cb830ea0fff29c34a22297d3c8926a0d3f"},"source":{"id":"2604.09500","kind":"arxiv","version":2},"verdict":{"id":"08d79e71-d351-49fb-a2de-da3e2a88561c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:57:37.753459Z","strongest_claim":"In the non-relativistic limit for the κ-Minkowski Dirac equation, the energy shift in the first excited state depends exclusively on the κ-parameter, and the non-relativistic limit introduces an orbital Zeeman coupling term for the fermionic fields.","one_line_summary":"Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The recently developed action principle for Lie-Poisson electrodynamics can be directly applied to derive conservation laws for the scalar and Dirac fields without introducing inconsistencies in the κ-Minkowski framework.","pith_extraction_headline":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.09500/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"08d79e71-d351-49fb-a2de-da3e2a88561c"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-20T00:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2c6PhyeH2D/59D/SzHPZomMN/RewaNcqdNnfkT5a4M4r7SvUXHglM4QV2FLJMuETIlugYIiuBM6lMCvtk3ORDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:32:04.240354Z"},"content_sha256":"d3d162e003c757492442db02640d10b62085a67ddd795d2c615fabaafd005866","schema_version":"1.0","event_id":"sha256:d3d162e003c757492442db02640d10b62085a67ddd795d2c615fabaafd005866"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/bundle.json","state_url":"https://pith.science/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T14:32:04Z","links":{"resolver":"https://pith.science/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES","bundle":"https://pith.science/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/bundle.json","state":"https://pith.science/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCJYS4YJBFMNTSPHUEAKMCF3ES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PCJYS4YJBFMNTSPHUEAKMCF3ES","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"477f081811551ef2b1aa84a4e82ce2484c4b4226a15c928c0fc44a3148cb9598","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-04-10T17:13:22Z","title_canon_sha256":"acb79d41c925f4aa958a78834d16673acb9d344ffd12c6ae9c53f5c9e6e24b5e"},"schema_version":"1.0","source":{"id":"2604.09500","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.09500","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"2604.09500v2","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.09500","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"PCJYS4YJBFMN","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_16","alias_value":"PCJYS4YJBFMNTSPH","created_at":"2026-07-20T00:18:20Z"},{"alias_kind":"pith_short_8","alias_value":"PCJYS4YJ","created_at":"2026-07-20T00:18:20Z"}],"graph_snapshots":[{"event_id":"sha256:d3d162e003c757492442db02640d10b62085a67ddd795d2c615fabaafd005866","target":"graph","created_at":"2026-07-20T00:18:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"In the non-relativistic limit for the κ-Minkowski Dirac equation, the energy shift in the first excited state depends exclusively on the κ-parameter, and the non-relativistic limit introduces an orbital Zeeman coupling term for the fermionic fields."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The recently developed action principle for Lie-Poisson electrodynamics can be directly applied to derive conservation laws for the scalar and Dirac fields without introducing inconsistencies in the κ-Minkowski framework."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case."}],"snapshot_sha256":"8d5c402f1b3471d800ddd397188a45cb830ea0fff29c34a22297d3c8926a0d3f"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.09500/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Poisson electrodynamics is the semiclassical limit of the full $U(1)$ non-commutative gauge theory, also known in recent literature as Poisson gauge theory. Two consolidated models for the theory studied in recent years, with a specific choice of non-commutative parameter, Lie-Poisson structures and constant ones, the later also known as the canonical, or Heisenberg case. In this paper, we present the theory considering the new building blocks related to symmetries and conservation laws, as a first step toward understanding the necessary mathematical tools to uncover some of the unknown pieces","authors_text":"M. J. Neves, O. Abla","cross_cats":[],"headline":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-04-10T17:13:22Z","title":"Conservation laws in classical Poisson field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.09500","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T16:57:37.753459Z","id":"08d79e71-d351-49fb-a2de-da3e2a88561c","model_set":{"reader":"grok-4.3"},"one_line_summary":"Conservation laws including energy-momentum tensor and charge are derived for Lie-Poisson field theories; the non-relativistic κ-Minkowski Dirac equation introduces an orbital Zeeman term whose energy shift depends only on the κ parameter.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Applying the Lie-Poisson electrodynamics action principle produces conservation laws for scalar and Dirac fields in κ-Minkowski spacetime, including a κ-only energy shift for the non-relativistic Dirac case.","strongest_claim":"In the non-relativistic limit for the κ-Minkowski Dirac equation, the energy shift in the first excited state depends exclusively on the κ-parameter, and the non-relativistic limit introduces an orbital Zeeman coupling term for the fermionic fields.","weakest_assumption":"The recently developed action principle for Lie-Poisson electrodynamics can be directly applied to derive conservation laws for the scalar and Dirac fields without introducing inconsistencies in the κ-Minkowski framework."}},"verdict_id":"08d79e71-d351-49fb-a2de-da3e2a88561c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a34b0161c049a96bc7044f819c7086877479c2af27d48d7ebb4c682332cb2f6c","target":"record","created_at":"2026-07-20T00:18:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"477f081811551ef2b1aa84a4e82ce2484c4b4226a15c928c0fc44a3148cb9598","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-04-10T17:13:22Z","title_canon_sha256":"acb79d41c925f4aa958a78834d16673acb9d344ffd12c6ae9c53f5c9e6e24b5e"},"schema_version":"1.0","source":{"id":"2604.09500","kind":"arxiv","version":2}},"canonical_sha256":"78938973090958d9c9e7a100a608bb24a039d23bfe3caca4922356665625bfa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78938973090958d9c9e7a100a608bb24a039d23bfe3caca4922356665625bfa5","first_computed_at":"2026-07-20T00:18:20.513483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T00:18:20.513483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Hoer6/xk01f2RRtcwJl1WeEiHezPJg1eVNzPFkhx9fPWGcnDW5KB7aDsY9OVI4jfeniYAlfjnN5+N6rNicMAQ==","signature_status":"signed_v1","signed_at":"2026-07-20T00:18:20.514493Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.09500","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a34b0161c049a96bc7044f819c7086877479c2af27d48d7ebb4c682332cb2f6c","sha256:d3d162e003c757492442db02640d10b62085a67ddd795d2c615fabaafd005866"],"state_sha256":"d09482e05a2f69004831da9ccc6b43dba2f63e87c6657d99cfe7167220145bf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UCJkmatPc7zoJDzr+qpIca+3/aaHHov8T3Tywa3NvQVB8oKS/mr5l21SBKR5EfYZFc1DsJrDo2bstbhbXLg7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:32:04.251810Z","bundle_sha256":"6315b086fa049b04c20ebf9114beea4ebbf636a4ab0f733132dc3d6939c5f882"}}