{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CML44JUNWDLX355CBVYOY34J5Q","short_pith_number":"pith:CML44JUN","schema_version":"1.0","canonical_sha256":"1317ce268db0d77df7a20d70ec6f89ec214d48253d7164c43408321dd7fb0bdc","source":{"kind":"arxiv","id":"2606.03004","version":1},"attestation_state":"computed","paper":{"title":"Kinematical correlations via $\\kappa$-Poincar\\'e coproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Babak Vakili, Mohammad Ali Gorji","submitted_at":"2026-06-02T01:21:42Z","abstract_excerpt":"We study a kinematical consequence of the Hopf-algebraic momentum composition law in $\\kappa$-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues $P_\\mu$ are nonlinearly related to the ordered-plane-wave labels $p_\\mu$. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.03004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-02T01:21:42Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"b3b129b1a1cf5d1746d683d07d64cf0d99c632e439891f0aed296b6189ae91c9","abstract_canon_sha256":"fddc22c54977497c51c4e6a44232f6ab6e2c7a7bf3f659a351d9df54ddda9943"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:29.032787Z","signature_b64":"9e3iQb7E63WdM3N+G6aR5TSPdD7L5DR/SLbfkxaBZCHbvaRB3z8vPHhl2oDfmP7WDH4yzI+uWs2qLKX7hQboDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1317ce268db0d77df7a20d70ec6f89ec214d48253d7164c43408321dd7fb0bdc","last_reissued_at":"2026-06-03T01:05:29.032368Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:29.032368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kinematical correlations via $\\kappa$-Poincar\\'e coproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Babak Vakili, Mohammad Ali Gorji","submitted_at":"2026-06-02T01:21:42Z","abstract_excerpt":"We study a kinematical consequence of the Hopf-algebraic momentum composition law in $\\kappa$-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues $P_\\mu$ are nonlinearly related to the ordered-plane-wave labels $p_\\mu$. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03004","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03004/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.03004","created_at":"2026-06-03T01:05:29.032447+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.03004v1","created_at":"2026-06-03T01:05:29.032447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03004","created_at":"2026-06-03T01:05:29.032447+00:00"},{"alias_kind":"pith_short_12","alias_value":"CML44JUNWDLX","created_at":"2026-06-03T01:05:29.032447+00:00"},{"alias_kind":"pith_short_16","alias_value":"CML44JUNWDLX355C","created_at":"2026-06-03T01:05:29.032447+00:00"},{"alias_kind":"pith_short_8","alias_value":"CML44JUN","created_at":"2026-06-03T01:05:29.032447+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q","json":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q.json","graph_json":"https://pith.science/api/pith-number/CML44JUNWDLX355CBVYOY34J5Q/graph.json","events_json":"https://pith.science/api/pith-number/CML44JUNWDLX355CBVYOY34J5Q/events.json","paper":"https://pith.science/paper/CML44JUN"},"agent_actions":{"view_html":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q","download_json":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q.json","view_paper":"https://pith.science/paper/CML44JUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.03004&json=true","fetch_graph":"https://pith.science/api/pith-number/CML44JUNWDLX355CBVYOY34J5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/CML44JUNWDLX355CBVYOY34J5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q/action/storage_attestation","attest_author":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q/action/author_attestation","sign_citation":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q/action/citation_signature","submit_replication":"https://pith.science/pith/CML44JUNWDLX355CBVYOY34J5Q/action/replication_record"}},"created_at":"2026-06-03T01:05:29.032447+00:00","updated_at":"2026-06-03T01:05:29.032447+00:00"}