{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZMR24KEJNYE26MUQXYJQDLVIJC","short_pith_number":"pith:ZMR24KEJ","canonical_record":{"source":{"id":"1006.1854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-06-09T16:39:16Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"025acede45e7b342f103805824944e46f26044e2740e2726f0081d072cbc7aa1","abstract_canon_sha256":"3a0c6577d9849b7be97b4a24970ab48d3f41ce9288615c3d16d8670892c02d36"},"schema_version":"1.0"},"canonical_sha256":"cb23ae28896e09af3290be1301aea848b9c31f20f2c72c374d6076fa5a2fbea7","source":{"kind":"arxiv","id":"1006.1854","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1854","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1854v1","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1854","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZMR24KEJNYE2","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZMR24KEJNYE26MUQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZMR24KEJ","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZMR24KEJNYE26MUQXYJQDLVIJC","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-06-09T16:39:16Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"025acede45e7b342f103805824944e46f26044e2740e2726f0081d072cbc7aa1","abstract_canon_sha256":"3a0c6577d9849b7be97b4a24970ab48d3f41ce9288615c3d16d8670892c02d36"},"schema_version":"1.0"},"canonical_sha256":"cb23ae28896e09af3290be1301aea848b9c31f20f2c72c374d6076fa5a2fbea7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:55.444041Z","signature_b64":"QplzVsRPq76YzLIx8KEClFeM2XzhhukgBUXPym4ekofKGoAXNWkrOf5DQU6DrmK/CdTZEaZCX3BDsWu0x+9eCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb23ae28896e09af3290be1301aea848b9c31f20f2c72c374d6076fa5a2fbea7","last_reissued_at":"2026-05-18T02:06:55.443431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:55.443431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1854","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":"2026-05-18T02:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXdG49Zyj8IaWwi8Rcl52fdD62xqXeRIPcxmdQnk7XJ3Do3mlhwRoi4RRZ1pj/222b2Jvmuev3a9D/Pi3psTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:49:19.675055Z"},"content_sha256":"08a5f7406613ddc58c2781def983b10fe1f0f628a828de235cc5444885c5284d","schema_version":"1.0","event_id":"sha256:08a5f7406613ddc58c2781def983b10fe1f0f628a828de235cc5444885c5284d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZMR24KEJNYE26MUQXYJQDLVIJC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"nlin.PS","authors_text":"L.I. Manevitch, V.V. Smirnov","submitted_at":"2010-06-09T16:39:16Z","abstract_excerpt":"We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns out to be twice more than threshold of zone boundary mode's instability. To obtain this result one needs in far going extension of the beating concept to a wide class of finite oscillatory chains. In turn,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1854","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":"2026-05-18T02:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ixc+ku1xZ5xyvAsJnYQ5zgTDHVKC348H0mDDII0Iy6qFdyVUZSTPLul1soBW3+x8aGRdgQ8m81MWeOxsqyK+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:49:19.675842Z"},"content_sha256":"7ab624ede810ac342d0b31eaa28cf8065ca2e06aa89c729f5b163acc52d9b4cf","schema_version":"1.0","event_id":"sha256:7ab624ede810ac342d0b31eaa28cf8065ca2e06aa89c729f5b163acc52d9b4cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/bundle.json","state_url":"https://pith.science/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/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":"2026-06-07T21:49:19Z","links":{"resolver":"https://pith.science/pith/ZMR24KEJNYE26MUQXYJQDLVIJC","bundle":"https://pith.science/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/bundle.json","state":"https://pith.science/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMR24KEJNYE26MUQXYJQDLVIJC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZMR24KEJNYE26MUQXYJQDLVIJC","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":"3a0c6577d9849b7be97b4a24970ab48d3f41ce9288615c3d16d8670892c02d36","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-06-09T16:39:16Z","title_canon_sha256":"025acede45e7b342f103805824944e46f26044e2740e2726f0081d072cbc7aa1"},"schema_version":"1.0","source":{"id":"1006.1854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1854","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1854v1","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1854","created_at":"2026-05-18T02:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZMR24KEJNYE2","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZMR24KEJNYE26MUQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZMR24KEJ","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:7ab624ede810ac342d0b31eaa28cf8065ca2e06aa89c729f5b163acc52d9b4cf","target":"graph","created_at":"2026-05-18T02:06:55Z","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 demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns out to be twice more than threshold of zone boundary mode's instability. To obtain this result one needs in far going extension of the beating concept to a wide class of finite oscillatory chains. In turn,","authors_text":"L.I. Manevitch, V.V. Smirnov","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-06-09T16:39:16Z","title":"Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1854","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":"sha256:08a5f7406613ddc58c2781def983b10fe1f0f628a828de235cc5444885c5284d","target":"record","created_at":"2026-05-18T02:06:55Z","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":"3a0c6577d9849b7be97b4a24970ab48d3f41ce9288615c3d16d8670892c02d36","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-06-09T16:39:16Z","title_canon_sha256":"025acede45e7b342f103805824944e46f26044e2740e2726f0081d072cbc7aa1"},"schema_version":"1.0","source":{"id":"1006.1854","kind":"arxiv","version":1}},"canonical_sha256":"cb23ae28896e09af3290be1301aea848b9c31f20f2c72c374d6076fa5a2fbea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb23ae28896e09af3290be1301aea848b9c31f20f2c72c374d6076fa5a2fbea7","first_computed_at":"2026-05-18T02:06:55.443431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:55.443431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QplzVsRPq76YzLIx8KEClFeM2XzhhukgBUXPym4ekofKGoAXNWkrOf5DQU6DrmK/CdTZEaZCX3BDsWu0x+9eCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:55.444041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a5f7406613ddc58c2781def983b10fe1f0f628a828de235cc5444885c5284d","sha256:7ab624ede810ac342d0b31eaa28cf8065ca2e06aa89c729f5b163acc52d9b4cf"],"state_sha256":"2c26d0d7e79face84cd00c107742547bee54ae1078dafb83fb07b4b237a7b542"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQD02wYhWu+LXNUGdOF2JK3Y93OikwLsXc/jWiSF+ClxV5mvP8GDdkmwmdcqam9ntYtGSn/MovJvBrgZ/+jMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:49:19.679682Z","bundle_sha256":"2b632588e7dc06b597a829ba86c3ac4065ee442fab9967c2b998213bc2a1f089"}}