{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZZM4K2K3WDO7RXBL2NALX5JCGU","short_pith_number":"pith:ZZM4K2K3","canonical_record":{"source":{"id":"1308.4745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T00:21:40Z","cross_cats_sorted":["math.DS","math.FA","math.MP"],"title_canon_sha256":"2f1af17547549f04f48c472af5fe51131fc6f2f24e8ff7fab27a57819d23ad6e","abstract_canon_sha256":"f29171164a0e26f2053750b177b9abbdd98cd3aa68470eb26063bb17c5141e9b"},"schema_version":"1.0"},"canonical_sha256":"ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b","source":{"kind":"arxiv","id":"1308.4745","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4745","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4745v1","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4745","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZZM4K2K3WDO7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZZM4K2K3WDO7RXBL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZZM4K2K3","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZZM4K2K3WDO7RXBL2NALX5JCGU","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T00:21:40Z","cross_cats_sorted":["math.DS","math.FA","math.MP"],"title_canon_sha256":"2f1af17547549f04f48c472af5fe51131fc6f2f24e8ff7fab27a57819d23ad6e","abstract_canon_sha256":"f29171164a0e26f2053750b177b9abbdd98cd3aa68470eb26063bb17c5141e9b"},"schema_version":"1.0"},"canonical_sha256":"ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:04.853926Z","signature_b64":"fbKCscZPs7RbNz99uvMqUNesIXgoqYyJFXb/fxDe56ybP4BBvtDi3bMtiHl03eWiR8QfpjGyi+6aipih30KVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b","last_reissued_at":"2026-05-18T01:48:04.853475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:04.853475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4745","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":"2026-05-18T01:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXrDQg49w/B/s0tZH4yGcERDFmqTdJijxLQdWom8zQ+mSkEY998hHvrvM/J2omPZfNEBwzprFD6OJ31w28/nAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:44:36.958012Z"},"content_sha256":"97bd64010b481c1eb718a44dabe50fd30456a1c8c79cb59d5b61a66cc492a3f1","schema_version":"1.0","event_id":"sha256:97bd64010b481c1eb718a44dabe50fd30456a1c8c79cb59d5b61a66cc492a3f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZZM4K2K3WDO7RXBL2NALX5JCGU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Penghui Wang, Xijun Hu, Yuwei Ou","submitted_at":"2013-08-22T00:21:40Z","abstract_excerpt":"In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4745","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":"2026-05-18T01:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tgjeudx3vH8zINgiJYcJC93fP+knYCKB/aAs8F8aazvMUnupdoWq07YPJkWpS6dcvcYHXujuTnkRinquCMjeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:44:36.958646Z"},"content_sha256":"c2f76fc2d415d985a394bc56cd72ae62b62305a8ba98d62de096fcee9aac6692","schema_version":"1.0","event_id":"sha256:c2f76fc2d415d985a394bc56cd72ae62b62305a8ba98d62de096fcee9aac6692"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/bundle.json","state_url":"https://pith.science/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/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":"2026-05-27T04:44:36Z","links":{"resolver":"https://pith.science/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU","bundle":"https://pith.science/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/bundle.json","state":"https://pith.science/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZM4K2K3WDO7RXBL2NALX5JCGU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZZM4K2K3WDO7RXBL2NALX5JCGU","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":"f29171164a0e26f2053750b177b9abbdd98cd3aa68470eb26063bb17c5141e9b","cross_cats_sorted":["math.DS","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T00:21:40Z","title_canon_sha256":"2f1af17547549f04f48c472af5fe51131fc6f2f24e8ff7fab27a57819d23ad6e"},"schema_version":"1.0","source":{"id":"1308.4745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4745","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4745v1","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4745","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZZM4K2K3WDO7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZZM4K2K3WDO7RXBL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZZM4K2K3","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:c2f76fc2d415d985a394bc56cd72ae62b62305a8ba98d62de096fcee9aac6692","target":"graph","created_at":"2026-05-18T01:48:04Z","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":"In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for t","authors_text":"Penghui Wang, Xijun Hu, Yuwei Ou","cross_cats":["math.DS","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T00:21:40Z","title":"Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4745","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":"sha256:97bd64010b481c1eb718a44dabe50fd30456a1c8c79cb59d5b61a66cc492a3f1","target":"record","created_at":"2026-05-18T01:48:04Z","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":"f29171164a0e26f2053750b177b9abbdd98cd3aa68470eb26063bb17c5141e9b","cross_cats_sorted":["math.DS","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T00:21:40Z","title_canon_sha256":"2f1af17547549f04f48c472af5fe51131fc6f2f24e8ff7fab27a57819d23ad6e"},"schema_version":"1.0","source":{"id":"1308.4745","kind":"arxiv","version":1}},"canonical_sha256":"ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b","first_computed_at":"2026-05-18T01:48:04.853475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:04.853475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fbKCscZPs7RbNz99uvMqUNesIXgoqYyJFXb/fxDe56ybP4BBvtDi3bMtiHl03eWiR8QfpjGyi+6aipih30KVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:04.853926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97bd64010b481c1eb718a44dabe50fd30456a1c8c79cb59d5b61a66cc492a3f1","sha256:c2f76fc2d415d985a394bc56cd72ae62b62305a8ba98d62de096fcee9aac6692"],"state_sha256":"46bbf221b174f500ecb7a8e2ec9db3a08954d27eb679291ff44aae5d79345fa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iQ9O/yLPQLoMWeR8Jb672L5IHZCFCpJv9LkMnCsobpNaJVamy2fnvSKhMDBA3qGf0p3Z1KLjWmFm8zqufy9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:44:36.961750Z","bundle_sha256":"101702a4da73eec3fb4649b4b8d4e8e58180d6b137d0378f53d731284c926add"}}