{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QBPX5SOF2MOS3747GYHS3KHQ4Z","short_pith_number":"pith:QBPX5SOF","canonical_record":{"source":{"id":"1602.05788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-02-18T13:22:24Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"0cf972ff71488216b9add7d8473c33189e0ae879dcd310245b7aa26649cb1ea2","abstract_canon_sha256":"bf34462e990fd568bc3053ce55cedd1c951f80dc5e9187b2abe51b84ba770a3b"},"schema_version":"1.0"},"canonical_sha256":"805f7ec9c5d31d2dff9f360f2da8f0e658eef83f3a5d554cfd77838c82734dae","source":{"kind":"arxiv","id":"1602.05788","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05788","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05788v2","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05788","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"QBPX5SOF2MOS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QBPX5SOF2MOS3747","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QBPX5SOF","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QBPX5SOF2MOS3747GYHS3KHQ4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-02-18T13:22:24Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"0cf972ff71488216b9add7d8473c33189e0ae879dcd310245b7aa26649cb1ea2","abstract_canon_sha256":"bf34462e990fd568bc3053ce55cedd1c951f80dc5e9187b2abe51b84ba770a3b"},"schema_version":"1.0"},"canonical_sha256":"805f7ec9c5d31d2dff9f360f2da8f0e658eef83f3a5d554cfd77838c82734dae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:45.073090Z","signature_b64":"0FE7PRv4UJ7PTIs05TTRfEo6bgaGYFBLOTn7gSgoXriINyf81Ik4Fbfpgq9xsGteI8deVmeN2QtcPcqZ3uINBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"805f7ec9c5d31d2dff9f360f2da8f0e658eef83f3a5d554cfd77838c82734dae","last_reissued_at":"2026-05-18T01:02:45.072610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:45.072610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05788","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":"2026-05-18T01:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AN3oHhhkybqcf4mDo7HloBX/qS4Lr5YQxbPUMHKi22dlyJegvpu0mdkEFI/bUeFJQA+RIsprL+m8KmNdYgnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:42:55.309155Z"},"content_sha256":"83831e8add1303acac5ca6d135869f6bb00573d878c84147d6a79c8ee0edf1c5","schema_version":"1.0","event_id":"sha256:83831e8add1303acac5ca6d135869f6bb00573d878c84147d6a79c8ee0edf1c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QBPX5SOF2MOS3747GYHS3KHQ4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformed phase spaces with group valued momenta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Francisco Nettel, Michele Arzano","submitted_at":"2016-02-18T13:22:24Z","abstract_excerpt":"We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the $n$-dimensional generalization of the $\\kappa$-deformed momentum space and the $SL(2, \\mathbb{R})$ momentu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05788","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uut1prAzI7neRuJQMDvI6u5XFoAfy/Gb5RfikF2nJ4dz/SrOGJ45L/QI0XCAH4Gtm8LhcA9NZMQ9S066cBN2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:42:55.309517Z"},"content_sha256":"4cf92b1c463d22eeedae2b9b62c31304ab7e58284ee8931f38192f61bcf65d6a","schema_version":"1.0","event_id":"sha256:4cf92b1c463d22eeedae2b9b62c31304ab7e58284ee8931f38192f61bcf65d6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/bundle.json","state_url":"https://pith.science/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/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":"2026-06-03T09:42:55Z","links":{"resolver":"https://pith.science/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z","bundle":"https://pith.science/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/bundle.json","state":"https://pith.science/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBPX5SOF2MOS3747GYHS3KHQ4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QBPX5SOF2MOS3747GYHS3KHQ4Z","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":"bf34462e990fd568bc3053ce55cedd1c951f80dc5e9187b2abe51b84ba770a3b","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-02-18T13:22:24Z","title_canon_sha256":"0cf972ff71488216b9add7d8473c33189e0ae879dcd310245b7aa26649cb1ea2"},"schema_version":"1.0","source":{"id":"1602.05788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05788","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05788v2","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05788","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"QBPX5SOF2MOS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QBPX5SOF2MOS3747","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QBPX5SOF","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4cf92b1c463d22eeedae2b9b62c31304ab7e58284ee8931f38192f61bcf65d6a","target":"graph","created_at":"2026-05-18T01:02:45Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the $n$-dimensional generalization of the $\\kappa$-deformed momentum space and the $SL(2, \\mathbb{R})$ momentu","authors_text":"Francisco Nettel, Michele Arzano","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-02-18T13:22:24Z","title":"Deformed phase spaces with group valued momenta"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05788","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83831e8add1303acac5ca6d135869f6bb00573d878c84147d6a79c8ee0edf1c5","target":"record","created_at":"2026-05-18T01:02:45Z","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":"bf34462e990fd568bc3053ce55cedd1c951f80dc5e9187b2abe51b84ba770a3b","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-02-18T13:22:24Z","title_canon_sha256":"0cf972ff71488216b9add7d8473c33189e0ae879dcd310245b7aa26649cb1ea2"},"schema_version":"1.0","source":{"id":"1602.05788","kind":"arxiv","version":2}},"canonical_sha256":"805f7ec9c5d31d2dff9f360f2da8f0e658eef83f3a5d554cfd77838c82734dae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"805f7ec9c5d31d2dff9f360f2da8f0e658eef83f3a5d554cfd77838c82734dae","first_computed_at":"2026-05-18T01:02:45.072610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:45.072610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0FE7PRv4UJ7PTIs05TTRfEo6bgaGYFBLOTn7gSgoXriINyf81Ik4Fbfpgq9xsGteI8deVmeN2QtcPcqZ3uINBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:45.073090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83831e8add1303acac5ca6d135869f6bb00573d878c84147d6a79c8ee0edf1c5","sha256:4cf92b1c463d22eeedae2b9b62c31304ab7e58284ee8931f38192f61bcf65d6a"],"state_sha256":"e0624c22829dbbf9d7286f90825f6c1bda2f441c36194d4c934fcf0605915052"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/W3eAv50yVg/Kpm1NuRmIgaiH8C8ygwN42Z+GlIe0jTs+hSd1BwDIrO6zfiv6MNBiM0wBwoCQsVgVbt2zKyYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:42:55.311501Z","bundle_sha256":"798185b78808b7bb32e4025f584ccd8f2f99e8187073f7b4a380c549d90d1e14"}}