{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NAB2BL3LOHL5K2JYW5U6GR3BZW","short_pith_number":"pith:NAB2BL3L","canonical_record":{"source":{"id":"1505.07552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-28T05:39:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e5c04cbddbe08237a7b3a7d471cd6a526c26fe2fa97039f9ce21e14f7f2a7a0a","abstract_canon_sha256":"fae0fd975a8215aa0e43a796d87c35586c33cdc8e6774a7467b1ba2549d7ab81"},"schema_version":"1.0"},"canonical_sha256":"6803a0af6b71d7d56938b769e34761cd8c7312cf6ebaa88b1047b29ab1c229ad","source":{"kind":"arxiv","id":"1505.07552","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07552","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07552v2","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07552","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"NAB2BL3LOHL5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NAB2BL3LOHL5K2JY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NAB2BL3L","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NAB2BL3LOHL5K2JYW5U6GR3BZW","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-28T05:39:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e5c04cbddbe08237a7b3a7d471cd6a526c26fe2fa97039f9ce21e14f7f2a7a0a","abstract_canon_sha256":"fae0fd975a8215aa0e43a796d87c35586c33cdc8e6774a7467b1ba2549d7ab81"},"schema_version":"1.0"},"canonical_sha256":"6803a0af6b71d7d56938b769e34761cd8c7312cf6ebaa88b1047b29ab1c229ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.810204Z","signature_b64":"g+XW1sC6mUTLwPTrQpEVb4oV6mb5eziPCodWKZat598ayXOlEgL9McXOjnlmWiDKxhOJ+WDzJM2MTy2vAoVYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6803a0af6b71d7d56938b769e34761cd8c7312cf6ebaa88b1047b29ab1c229ad","last_reissued_at":"2026-05-18T01:23:18.809629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.809629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07552","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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyCqbZ3OMQfIzcBZQh1xT7D/geJETBMuvuxvU0wb9m9tWeUAnXvQEb9zM/Ugz/uYN4PSau8TxLEGXEX6KZFqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:14:38.069271Z"},"content_sha256":"ed8560369b849d5e5ae807c50bc60c586861dc6f80ba3db4a8d7c0859182d40c","schema_version":"1.0","event_id":"sha256:ed8560369b849d5e5ae807c50bc60c586861dc6f80ba3db4a8d7c0859182d40c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NAB2BL3LOHL5K2JYW5U6GR3BZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploring Branched Hamiltonians for a Class of Nonlinear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bijan Bagchi, Franti\\v{s}ek Ruzicka, Miloslav Znojil, Prasanta K. Panigrahi, Subhrajit Modak","submitted_at":"2015-05-28T05:39:03Z","abstract_excerpt":"One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Lienard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07552","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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8LIvSbouEos/gIP09oMTWahTSC/8BLCgfYYeEFmipLK1GO/lV1oT0+ENt2UlLgMF6VbqL8ueqeTL3tdUNyEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:14:38.069642Z"},"content_sha256":"8d1a0c5ca1d8b5f3ae8c8a217f36c68be5003b08df308704e95c0297c8c12633","schema_version":"1.0","event_id":"sha256:8d1a0c5ca1d8b5f3ae8c8a217f36c68be5003b08df308704e95c0297c8c12633"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/bundle.json","state_url":"https://pith.science/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/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":"2026-05-25T04:14:38Z","links":{"resolver":"https://pith.science/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW","bundle":"https://pith.science/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/bundle.json","state":"https://pith.science/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NAB2BL3LOHL5K2JYW5U6GR3BZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NAB2BL3LOHL5K2JYW5U6GR3BZW","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":"fae0fd975a8215aa0e43a796d87c35586c33cdc8e6774a7467b1ba2549d7ab81","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-28T05:39:03Z","title_canon_sha256":"e5c04cbddbe08237a7b3a7d471cd6a526c26fe2fa97039f9ce21e14f7f2a7a0a"},"schema_version":"1.0","source":{"id":"1505.07552","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07552","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07552v2","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07552","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"NAB2BL3LOHL5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NAB2BL3LOHL5K2JY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NAB2BL3L","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:8d1a0c5ca1d8b5f3ae8c8a217f36c68be5003b08df308704e95c0297c8c12633","target":"graph","created_at":"2026-05-18T01:23:18Z","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":"One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Lienard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.","authors_text":"Bijan Bagchi, Franti\\v{s}ek Ruzicka, Miloslav Znojil, Prasanta K. Panigrahi, Subhrajit Modak","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-28T05:39:03Z","title":"Exploring Branched Hamiltonians for a Class of Nonlinear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07552","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:ed8560369b849d5e5ae807c50bc60c586861dc6f80ba3db4a8d7c0859182d40c","target":"record","created_at":"2026-05-18T01:23:18Z","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":"fae0fd975a8215aa0e43a796d87c35586c33cdc8e6774a7467b1ba2549d7ab81","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-28T05:39:03Z","title_canon_sha256":"e5c04cbddbe08237a7b3a7d471cd6a526c26fe2fa97039f9ce21e14f7f2a7a0a"},"schema_version":"1.0","source":{"id":"1505.07552","kind":"arxiv","version":2}},"canonical_sha256":"6803a0af6b71d7d56938b769e34761cd8c7312cf6ebaa88b1047b29ab1c229ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6803a0af6b71d7d56938b769e34761cd8c7312cf6ebaa88b1047b29ab1c229ad","first_computed_at":"2026-05-18T01:23:18.809629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:18.809629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g+XW1sC6mUTLwPTrQpEVb4oV6mb5eziPCodWKZat598ayXOlEgL9McXOjnlmWiDKxhOJ+WDzJM2MTy2vAoVYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:18.810204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07552","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed8560369b849d5e5ae807c50bc60c586861dc6f80ba3db4a8d7c0859182d40c","sha256:8d1a0c5ca1d8b5f3ae8c8a217f36c68be5003b08df308704e95c0297c8c12633"],"state_sha256":"f5b2c61b5b572e75ca7028cd334252a23141e71cedd4cbde4dc4f2152ce3b0c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y349TTYxWoK4sjM2t2NvivE6sKHmCsBv+/4FK8D83ERUZIUkO31mBncV0kfjQ7pvLkKKcNVMKpnQMHIbbAnZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:14:38.072233Z","bundle_sha256":"43678ab9f6fa87b5bf18466b7ab26e45fe3e30f3c78128d9b647c25550549ca5"}}