{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2D5UFGVKO5WZLAVMATFUZOMNFS","short_pith_number":"pith:2D5UFGVK","canonical_record":{"source":{"id":"1204.3909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-04-17T20:24:42Z","cross_cats_sorted":[],"title_canon_sha256":"a8d4616b806c0f9392e055bfb8bfe92cbc93f3c1c175c6c6f8b2a6c485f1add2","abstract_canon_sha256":"8419ff75332d8540e0f519ab31badcc120856c7ae6e5f8fa89c40c729e3b7b00"},"schema_version":"1.0"},"canonical_sha256":"d0fb429aaa776d9582ac04cb4cb98d2cb5f91c208111c35540a073516afff9cf","source":{"kind":"arxiv","id":"1204.3909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3909","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3909v1","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3909","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"2D5UFGVKO5WZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2D5UFGVKO5WZLAVM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2D5UFGVK","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2D5UFGVKO5WZLAVMATFUZOMNFS","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-04-17T20:24:42Z","cross_cats_sorted":[],"title_canon_sha256":"a8d4616b806c0f9392e055bfb8bfe92cbc93f3c1c175c6c6f8b2a6c485f1add2","abstract_canon_sha256":"8419ff75332d8540e0f519ab31badcc120856c7ae6e5f8fa89c40c729e3b7b00"},"schema_version":"1.0"},"canonical_sha256":"d0fb429aaa776d9582ac04cb4cb98d2cb5f91c208111c35540a073516afff9cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:49.688762Z","signature_b64":"xqcaJDZH4TLNCGAPbq5EKu66dwTT3u33HBRyI4l5bbIfFjrJNX3pMQIMRJwZ0th0Ykd6EPJoTenys/aa5oKzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0fb429aaa776d9582ac04cb4cb98d2cb5f91c208111c35540a073516afff9cf","last_reissued_at":"2026-05-18T01:57:49.688271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:49.688271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3909","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":"2026-05-18T01:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBKejATot6tu5c/3jd1qVddStUq+AkDVgtNE44uFele1xYJXNX9NXa0D6pRMCtn0Ln0LWOQ9RNdxQqTFMMxkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:22:17.922610Z"},"content_sha256":"4681b4860ea31ddb0dfbe2b97ccb7265a0b21c2aaa98150fc61dbc525f011633","schema_version":"1.0","event_id":"sha256:4681b4860ea31ddb0dfbe2b97ccb7265a0b21c2aaa98150fc61dbc525f011633"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2D5UFGVKO5WZLAVMATFUZOMNFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic Travelling Waves in Dimer Granular Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Dmitry E. Pelinovsky, Matthew Betti","submitted_at":"2012-04-17T20:24:42Z","abstract_excerpt":"We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3909","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":"2026-05-18T01:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBY99WcE8x2rP5QuhudkvFcoStKcPZ4M0ozNkNVzOtA/l7VphnobrSiXb0wiB3tYwuSGHjDMPw0mn7Th5LpEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:22:17.923303Z"},"content_sha256":"2642862f5344c025b6b0ca3747c8dd086203c0b7f4f582b5ad51bab75d171660","schema_version":"1.0","event_id":"sha256:2642862f5344c025b6b0ca3747c8dd086203c0b7f4f582b5ad51bab75d171660"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/bundle.json","state_url":"https://pith.science/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/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":"2026-05-27T04:22:17Z","links":{"resolver":"https://pith.science/pith/2D5UFGVKO5WZLAVMATFUZOMNFS","bundle":"https://pith.science/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/bundle.json","state":"https://pith.science/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2D5UFGVKO5WZLAVMATFUZOMNFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2D5UFGVKO5WZLAVMATFUZOMNFS","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":"8419ff75332d8540e0f519ab31badcc120856c7ae6e5f8fa89c40c729e3b7b00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-04-17T20:24:42Z","title_canon_sha256":"a8d4616b806c0f9392e055bfb8bfe92cbc93f3c1c175c6c6f8b2a6c485f1add2"},"schema_version":"1.0","source":{"id":"1204.3909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3909","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3909v1","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3909","created_at":"2026-05-18T01:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"2D5UFGVKO5WZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2D5UFGVKO5WZLAVM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2D5UFGVK","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:2642862f5344c025b6b0ca3747c8dd086203c0b7f4f582b5ad51bab75d171660","target":"graph","created_at":"2026-05-18T01:57:49Z","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 study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist.","authors_text":"Dmitry E. Pelinovsky, Matthew Betti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-04-17T20:24:42Z","title":"Periodic Travelling Waves in Dimer Granular Chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3909","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":"sha256:4681b4860ea31ddb0dfbe2b97ccb7265a0b21c2aaa98150fc61dbc525f011633","target":"record","created_at":"2026-05-18T01:57:49Z","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":"8419ff75332d8540e0f519ab31badcc120856c7ae6e5f8fa89c40c729e3b7b00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-04-17T20:24:42Z","title_canon_sha256":"a8d4616b806c0f9392e055bfb8bfe92cbc93f3c1c175c6c6f8b2a6c485f1add2"},"schema_version":"1.0","source":{"id":"1204.3909","kind":"arxiv","version":1}},"canonical_sha256":"d0fb429aaa776d9582ac04cb4cb98d2cb5f91c208111c35540a073516afff9cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0fb429aaa776d9582ac04cb4cb98d2cb5f91c208111c35540a073516afff9cf","first_computed_at":"2026-05-18T01:57:49.688271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:49.688271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xqcaJDZH4TLNCGAPbq5EKu66dwTT3u33HBRyI4l5bbIfFjrJNX3pMQIMRJwZ0th0Ykd6EPJoTenys/aa5oKzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:49.688762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4681b4860ea31ddb0dfbe2b97ccb7265a0b21c2aaa98150fc61dbc525f011633","sha256:2642862f5344c025b6b0ca3747c8dd086203c0b7f4f582b5ad51bab75d171660"],"state_sha256":"b8a47eabb290ab781a38af5636e6aba172e4704abf76827f5757ee3e39b6028c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXY+FhwRayrLLZ1ECGZ+oWAkl9Wz/bVrVoWH9PCnWkEhNX3vBXqgPgfvlOgUr6gxFIWi5F+q9s6+GkPtWm0GBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:22:17.926782Z","bundle_sha256":"c5788e04fcfbcc4bd9091e8f7b0788ee09ca8f9ce7f61dff605ad517563897fe"}}