{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B6TGLPRGNC2Y4E7J4SMNUMP3ZA","short_pith_number":"pith:B6TGLPRG","canonical_record":{"source":{"id":"1205.3330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-15T11:24:10Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"5b541bb72c6cceaaa66f0c13ee9d2c274a7254509581fbd0477d8c5553a9d03b","abstract_canon_sha256":"bcb96f10c180c0dc9cdccf6901e19b4ad7f1d5b9f0d04201e78673d0c2b505f2"},"schema_version":"1.0"},"canonical_sha256":"0fa665be2668b58e13e9e498da31fbc81a5be9d9f351ccce4b7ba5818fca6c60","source":{"kind":"arxiv","id":"1205.3330","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3330","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3330v1","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3330","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"B6TGLPRGNC2Y","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6TGLPRGNC2Y4E7J","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6TGLPRG","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B6TGLPRGNC2Y4E7J4SMNUMP3ZA","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-15T11:24:10Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"5b541bb72c6cceaaa66f0c13ee9d2c274a7254509581fbd0477d8c5553a9d03b","abstract_canon_sha256":"bcb96f10c180c0dc9cdccf6901e19b4ad7f1d5b9f0d04201e78673d0c2b505f2"},"schema_version":"1.0"},"canonical_sha256":"0fa665be2668b58e13e9e498da31fbc81a5be9d9f351ccce4b7ba5818fca6c60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:32.063032Z","signature_b64":"n2uVRVfLPA+kE3ZMEAvUskphifIG6ggcOO9xa6lYLlhUrRKmrPZyJDxr94FUD7aT5qTuvvt2xhasv5o47zx7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fa665be2668b58e13e9e498da31fbc81a5be9d9f351ccce4b7ba5818fca6c60","last_reissued_at":"2026-05-18T01:57:32.062537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:32.062537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3330","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":"2026-05-18T01:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0YNtpXZns86uMQgZXP1YR1bVpf2FO/xJIx/2YIUkbLmLjJLlezREyfV0AI7JG65jnT9ohPPZwddVKxOStOvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:23:16.228879Z"},"content_sha256":"3c34fdd2e7627968393a00b48db5d7de1614018d7a8d36dd973e2462342cc111","schema_version":"1.0","event_id":"sha256:3c34fdd2e7627968393a00b48db5d7de1614018d7a8d36dd973e2462342cc111"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B6TGLPRGNC2Y4E7J4SMNUMP3ZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex Trajectories in a Classical Periodic Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Alexander G. Anderson, Carl M. Bender","submitted_at":"2012-05-15T11:24:10Z","abstract_excerpt":"This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3330","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":"2026-05-18T01:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHRWuyCBRM+AaCfds6Vm/XM2plZetZIZsjIlJFyQmxlDUJYGx+gq738bQoV/L8fJVxpClBeb/aAmxgJbNxxdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:23:16.229242Z"},"content_sha256":"29f9d7d2db34902078b5fc82188af018149895c4239ab35014dd4ea63f8a4d3c","schema_version":"1.0","event_id":"sha256:29f9d7d2db34902078b5fc82188af018149895c4239ab35014dd4ea63f8a4d3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/bundle.json","state_url":"https://pith.science/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/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":"2026-05-24T06:23:16Z","links":{"resolver":"https://pith.science/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA","bundle":"https://pith.science/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/bundle.json","state":"https://pith.science/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6TGLPRGNC2Y4E7J4SMNUMP3ZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B6TGLPRGNC2Y4E7J4SMNUMP3ZA","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":"bcb96f10c180c0dc9cdccf6901e19b4ad7f1d5b9f0d04201e78673d0c2b505f2","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-15T11:24:10Z","title_canon_sha256":"5b541bb72c6cceaaa66f0c13ee9d2c274a7254509581fbd0477d8c5553a9d03b"},"schema_version":"1.0","source":{"id":"1205.3330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3330","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3330v1","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3330","created_at":"2026-05-18T01:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"B6TGLPRGNC2Y","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6TGLPRGNC2Y4E7J","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6TGLPRG","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:29f9d7d2db34902078b5fc82188af018149895c4239ab35014dd4ea63f8a4d3c","target":"graph","created_at":"2026-05-18T01:57:32Z","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":"This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a re","authors_text":"Alexander G. Anderson, Carl M. Bender","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-15T11:24:10Z","title":"Complex Trajectories in a Classical Periodic Potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3330","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":"sha256:3c34fdd2e7627968393a00b48db5d7de1614018d7a8d36dd973e2462342cc111","target":"record","created_at":"2026-05-18T01:57:32Z","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":"bcb96f10c180c0dc9cdccf6901e19b4ad7f1d5b9f0d04201e78673d0c2b505f2","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-15T11:24:10Z","title_canon_sha256":"5b541bb72c6cceaaa66f0c13ee9d2c274a7254509581fbd0477d8c5553a9d03b"},"schema_version":"1.0","source":{"id":"1205.3330","kind":"arxiv","version":1}},"canonical_sha256":"0fa665be2668b58e13e9e498da31fbc81a5be9d9f351ccce4b7ba5818fca6c60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fa665be2668b58e13e9e498da31fbc81a5be9d9f351ccce4b7ba5818fca6c60","first_computed_at":"2026-05-18T01:57:32.062537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:32.062537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n2uVRVfLPA+kE3ZMEAvUskphifIG6ggcOO9xa6lYLlhUrRKmrPZyJDxr94FUD7aT5qTuvvt2xhasv5o47zx7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:32.063032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c34fdd2e7627968393a00b48db5d7de1614018d7a8d36dd973e2462342cc111","sha256:29f9d7d2db34902078b5fc82188af018149895c4239ab35014dd4ea63f8a4d3c"],"state_sha256":"41a4c385f3bf2503e6c013d2faaa87c9a11b4d936e373d43ae19e19519010b8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJKoos/oidLcfb9HAGk4pLE59tbjLZPX2L/ieSNmQGBu0eHh+3ODoxGLprGw1zflc2rJGBllP+V3joKVcfwVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T06:23:16.233137Z","bundle_sha256":"bcf11019f3b9b1a3c08b5840b604795822e2c786d5da208b74dad4d84caeefc3"}}