{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GQ4X5EEDIH7RROECVEWOJEW5F7","short_pith_number":"pith:GQ4X5EED","canonical_record":{"source":{"id":"1601.00436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-01-04T10:18:14Z","cross_cats_sorted":[],"title_canon_sha256":"c2a12eb5287f049764f7905ad0696b37e87bd9c2e6fc255b76f90cd02e89bde4","abstract_canon_sha256":"3f2277481fcd86075c543358e448231e80833cea04493ebb8f66bcb12cc9f495"},"schema_version":"1.0"},"canonical_sha256":"34397e908341ff18b882a92ce492dd2fe06dcd2f3ba899ae8f3ca0408f9768b8","source":{"kind":"arxiv","id":"1601.00436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00436","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00436v1","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00436","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"pith_short_12","alias_value":"GQ4X5EEDIH7R","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GQ4X5EEDIH7RROEC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GQ4X5EED","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GQ4X5EEDIH7RROECVEWOJEW5F7","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-01-04T10:18:14Z","cross_cats_sorted":[],"title_canon_sha256":"c2a12eb5287f049764f7905ad0696b37e87bd9c2e6fc255b76f90cd02e89bde4","abstract_canon_sha256":"3f2277481fcd86075c543358e448231e80833cea04493ebb8f66bcb12cc9f495"},"schema_version":"1.0"},"canonical_sha256":"34397e908341ff18b882a92ce492dd2fe06dcd2f3ba899ae8f3ca0408f9768b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:27.457269Z","signature_b64":"CGShMusit+smgrwlCzM2fUn6XRoIam/CeD7JHgpiOpD+wIijL0Nz9d7GjkYNUZjDWPD7Y6EvhYIqAhGb5YwqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34397e908341ff18b882a92ce492dd2fe06dcd2f3ba899ae8f3ca0408f9768b8","last_reissued_at":"2026-05-18T01:23:27.456734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:27.456734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00436","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWKXxfHlPGBoLmfdH8MiU+9ohoVli/Nb+uyCmUvlG7Kfin7KfoDS8j9QgVkEWHIon2JNqyBTIKJagESBL8A5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:47.723601Z"},"content_sha256":"388f90e4a27571351fc9f477a759d8cbb1d3e3ee30f356a58380ff3a43872576","schema_version":"1.0","event_id":"sha256:388f90e4a27571351fc9f477a759d8cbb1d3e3ee30f356a58380ff3a43872576"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GQ4X5EEDIH7RROECVEWOJEW5F7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction and counting of the number of operators included in a normalized vibrational Hamiltonian with n degrees of freedom with a p:q resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. Leroy, G. Saget, H.R. Jauslin","submitted_at":"2016-01-04T10:18:14Z","abstract_excerpt":"We propose a method of construction of a normalized vibrational Hamiltonian of a highly excited molecular system with $n$ degrees of freedom in the case of a a $p:q$ resonance. We present also the counting of all the independent operators and the counting of all the parameters included in the Hamiltonian (Counting theorems 1 to 8). The method introduces, on a systematic way, all the operators, in particular the coupling operators, that can be built from the polynomials formed by products of powers of the generators of a Lie algebra: the algebra of the invariant polynomials built in classical m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00436","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":""},"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":"2026-05-18T01:23:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGGlhx8z8CjQSEJ04Syjh8Sw4lzZv0Mjl/EtQ7+o7n8Zh2ePcQUlq5KX5Sj8QGM0nT5K3+QBfLvp6/NDHO52Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:47.724279Z"},"content_sha256":"b2603cb4b34a83debf45871b0ef43adf15076f668682ee074d028ec2e652219e","schema_version":"1.0","event_id":"sha256:b2603cb4b34a83debf45871b0ef43adf15076f668682ee074d028ec2e652219e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/bundle.json","state_url":"https://pith.science/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/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":"2026-06-07T23:08:47Z","links":{"resolver":"https://pith.science/pith/GQ4X5EEDIH7RROECVEWOJEW5F7","bundle":"https://pith.science/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/bundle.json","state":"https://pith.science/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQ4X5EEDIH7RROECVEWOJEW5F7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GQ4X5EEDIH7RROECVEWOJEW5F7","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":"3f2277481fcd86075c543358e448231e80833cea04493ebb8f66bcb12cc9f495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-01-04T10:18:14Z","title_canon_sha256":"c2a12eb5287f049764f7905ad0696b37e87bd9c2e6fc255b76f90cd02e89bde4"},"schema_version":"1.0","source":{"id":"1601.00436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00436","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00436v1","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00436","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"pith_short_12","alias_value":"GQ4X5EEDIH7R","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GQ4X5EEDIH7RROEC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GQ4X5EED","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:b2603cb4b34a83debf45871b0ef43adf15076f668682ee074d028ec2e652219e","target":"graph","created_at":"2026-05-18T01:23:27Z","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 propose a method of construction of a normalized vibrational Hamiltonian of a highly excited molecular system with $n$ degrees of freedom in the case of a a $p:q$ resonance. We present also the counting of all the independent operators and the counting of all the parameters included in the Hamiltonian (Counting theorems 1 to 8). The method introduces, on a systematic way, all the operators, in particular the coupling operators, that can be built from the polynomials formed by products of powers of the generators of a Lie algebra: the algebra of the invariant polynomials built in classical m","authors_text":"C. Leroy, G. Saget, H.R. Jauslin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-01-04T10:18:14Z","title":"Construction and counting of the number of operators included in a normalized vibrational Hamiltonian with n degrees of freedom with a p:q resonance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00436","kind":"arxiv","version":1},"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":"sha256:388f90e4a27571351fc9f477a759d8cbb1d3e3ee30f356a58380ff3a43872576","target":"record","created_at":"2026-05-18T01:23:27Z","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":"3f2277481fcd86075c543358e448231e80833cea04493ebb8f66bcb12cc9f495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-01-04T10:18:14Z","title_canon_sha256":"c2a12eb5287f049764f7905ad0696b37e87bd9c2e6fc255b76f90cd02e89bde4"},"schema_version":"1.0","source":{"id":"1601.00436","kind":"arxiv","version":1}},"canonical_sha256":"34397e908341ff18b882a92ce492dd2fe06dcd2f3ba899ae8f3ca0408f9768b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34397e908341ff18b882a92ce492dd2fe06dcd2f3ba899ae8f3ca0408f9768b8","first_computed_at":"2026-05-18T01:23:27.456734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:27.456734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGShMusit+smgrwlCzM2fUn6XRoIam/CeD7JHgpiOpD+wIijL0Nz9d7GjkYNUZjDWPD7Y6EvhYIqAhGb5YwqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:27.457269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:388f90e4a27571351fc9f477a759d8cbb1d3e3ee30f356a58380ff3a43872576","sha256:b2603cb4b34a83debf45871b0ef43adf15076f668682ee074d028ec2e652219e"],"state_sha256":"c5a13530de951aca9a137d5f639ab435b7c0bd026fa857081b5370d1ab45db08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGS9JaHZFQrOSzGFfb2+HFuMeV5Bd9fHsh6ppWT8mhD70eidXVfqg2G7+lFq/uk929RnAUGO6aeLh8VvDK+iDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:08:47.727614Z","bundle_sha256":"5a3dfccb8dfd57341e52862ceca5d0c2a5419f9dc0d73525c3202c8e8af23ffe"}}