{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WLH4SSVTGNHCXU67X7DQ43WWMU","short_pith_number":"pith:WLH4SSVT","canonical_record":{"source":{"id":"1210.5173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-10-18T16:23:12Z","cross_cats_sorted":[],"title_canon_sha256":"f2dd7465e47ba8902a5c7d48cbbdff9c3238cc595a582134ce6389da471b7910","abstract_canon_sha256":"292fbe10234c4d98f510e7d050a1533cfce4a0c7159e5ef0c85c5ba71eec6216"},"schema_version":"1.0"},"canonical_sha256":"b2cfc94ab3334e2bd3dfbfc70e6ed6652abe15dd6dc8a494108278b85abbeb33","source":{"kind":"arxiv","id":"1210.5173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5173","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5173v1","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5173","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"WLH4SSVTGNHC","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WLH4SSVTGNHCXU67","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WLH4SSVT","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WLH4SSVTGNHCXU67X7DQ43WWMU","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-10-18T16:23:12Z","cross_cats_sorted":[],"title_canon_sha256":"f2dd7465e47ba8902a5c7d48cbbdff9c3238cc595a582134ce6389da471b7910","abstract_canon_sha256":"292fbe10234c4d98f510e7d050a1533cfce4a0c7159e5ef0c85c5ba71eec6216"},"schema_version":"1.0"},"canonical_sha256":"b2cfc94ab3334e2bd3dfbfc70e6ed6652abe15dd6dc8a494108278b85abbeb33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:46.472003Z","signature_b64":"COdQtaVYl7GnPB+DCQWqcf2HfAHiBbNf22MBGqYqKEaJxA42jQKlASUeneM1AykDhUMxYxEMt4gsPV4BO5QxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2cfc94ab3334e2bd3dfbfc70e6ed6652abe15dd6dc8a494108278b85abbeb33","last_reissued_at":"2026-05-18T01:53:46.471377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:46.471377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5173","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":"2026-05-18T01:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RGzgmE5jUUEhGkcBmQejE2aFKmrNKiLkbX1nj2Tj3gmlYtfbZvP+wAm9qV3w788RXAZjSrKnkzmHbWgafSDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:30:13.262168Z"},"content_sha256":"dcf0ee7714833795e353af8b564532e313629220a0b5af4cd24d0c197eb01341","schema_version":"1.0","event_id":"sha256:dcf0ee7714833795e353af8b564532e313629220a0b5af4cd24d0c197eb01341"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WLH4SSVTGNHCXU67X7DQ43WWMU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dark Breathers in Granular Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"C. Chong, Chiara Daraio, G. Theocharis, P.G. Kevrekidis","submitted_at":"2012-10-18T16:23:12Z","abstract_excerpt":"We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5173","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":"2026-05-18T01:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OJaMvKwCYCKrt6vj9zTD3GSjQXcPZdKMpdEqt9NawY88kTY6BQ0crsX/qU7R602gBDzp9t/TDmlqVCbebgBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:30:13.262850Z"},"content_sha256":"f87e854c1b4e007b798381010c3fc9ef933128173b39887a2123e656a7f2acd0","schema_version":"1.0","event_id":"sha256:f87e854c1b4e007b798381010c3fc9ef933128173b39887a2123e656a7f2acd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/bundle.json","state_url":"https://pith.science/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/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":"2026-05-30T01:30:13Z","links":{"resolver":"https://pith.science/pith/WLH4SSVTGNHCXU67X7DQ43WWMU","bundle":"https://pith.science/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/bundle.json","state":"https://pith.science/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WLH4SSVTGNHCXU67X7DQ43WWMU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WLH4SSVTGNHCXU67X7DQ43WWMU","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":"292fbe10234c4d98f510e7d050a1533cfce4a0c7159e5ef0c85c5ba71eec6216","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-10-18T16:23:12Z","title_canon_sha256":"f2dd7465e47ba8902a5c7d48cbbdff9c3238cc595a582134ce6389da471b7910"},"schema_version":"1.0","source":{"id":"1210.5173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5173","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5173v1","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5173","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"WLH4SSVTGNHC","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WLH4SSVTGNHCXU67","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WLH4SSVT","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f87e854c1b4e007b798381010c3fc9ef933128173b39887a2123e656a7f2acd0","target":"graph","created_at":"2026-05-18T01:53:46Z","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 present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to th","authors_text":"C. Chong, Chiara Daraio, G. Theocharis, P.G. Kevrekidis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-10-18T16:23:12Z","title":"Dark Breathers in Granular Crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5173","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:dcf0ee7714833795e353af8b564532e313629220a0b5af4cd24d0c197eb01341","target":"record","created_at":"2026-05-18T01:53:46Z","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":"292fbe10234c4d98f510e7d050a1533cfce4a0c7159e5ef0c85c5ba71eec6216","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-10-18T16:23:12Z","title_canon_sha256":"f2dd7465e47ba8902a5c7d48cbbdff9c3238cc595a582134ce6389da471b7910"},"schema_version":"1.0","source":{"id":"1210.5173","kind":"arxiv","version":1}},"canonical_sha256":"b2cfc94ab3334e2bd3dfbfc70e6ed6652abe15dd6dc8a494108278b85abbeb33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2cfc94ab3334e2bd3dfbfc70e6ed6652abe15dd6dc8a494108278b85abbeb33","first_computed_at":"2026-05-18T01:53:46.471377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:46.471377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COdQtaVYl7GnPB+DCQWqcf2HfAHiBbNf22MBGqYqKEaJxA42jQKlASUeneM1AykDhUMxYxEMt4gsPV4BO5QxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:46.472003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcf0ee7714833795e353af8b564532e313629220a0b5af4cd24d0c197eb01341","sha256:f87e854c1b4e007b798381010c3fc9ef933128173b39887a2123e656a7f2acd0"],"state_sha256":"6ff990677cbe627988f173b587e0da717e08df041fed1231490a62bcc74aab7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gU5iOqLOzDj1++Ur8BmBOwBm/ziRqNHm6OHKt3LO+ADp5DCWPTEJpaTL/5PwiO3U/IuDDSzoBnwHP6G2hyyAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:30:13.267348Z","bundle_sha256":"24a0491b3310e69dcc65abf109d55cb93453f80ee43b6ac2c123cf0e699b03df"}}