{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DKXGS6H25RAYNC4EGQRX2KUXQP","short_pith_number":"pith:DKXGS6H2","canonical_record":{"source":{"id":"1105.3364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-05-17T13:12:31Z","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"title_canon_sha256":"8ec5d4b35f5af4bea94a0629a338e0e5ee095a3c649aa428869e3fbbafb1ad6b","abstract_canon_sha256":"e72803d1673982671efacd638d93c6d23290501550172267bc7931411e4e0509"},"schema_version":"1.0"},"canonical_sha256":"1aae6978faec41868b8434237d2a9783d8013937edac598b944e33d1ddfa392f","source":{"kind":"arxiv","id":"1105.3364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3364","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3364v1","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3364","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"pith_short_12","alias_value":"DKXGS6H25RAY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DKXGS6H25RAYNC4E","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DKXGS6H2","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DKXGS6H25RAYNC4EGQRX2KUXQP","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-05-17T13:12:31Z","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"title_canon_sha256":"8ec5d4b35f5af4bea94a0629a338e0e5ee095a3c649aa428869e3fbbafb1ad6b","abstract_canon_sha256":"e72803d1673982671efacd638d93c6d23290501550172267bc7931411e4e0509"},"schema_version":"1.0"},"canonical_sha256":"1aae6978faec41868b8434237d2a9783d8013937edac598b944e33d1ddfa392f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:57.229669Z","signature_b64":"fgAOPqDZFNg+/3wyT4z6WZJMxpe8o87SmbDPTtB2Z2JnjwPSfTKSv6CmMDPUlY6OnfZXHaDpMtR14vwtIebMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aae6978faec41868b8434237d2a9783d8013937edac598b944e33d1ddfa392f","last_reissued_at":"2026-05-18T02:01:57.228882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:57.228882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3364","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":"2026-05-18T02:01:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRC2zg2idOMG3nAAaOhqp9QC16Av7t5vHXWouvrU7A6ip1ui9UTeVGOxnJkrQMghc0/8lrSdIu6LlbujBXruCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T10:39:59.007294Z"},"content_sha256":"419e4296e3e7ef8e6ab6a9a69805e77351f0ee103fc04d916b98d75cd4bd933a","schema_version":"1.0","event_id":"sha256:419e4296e3e7ef8e6ab6a9a69805e77351f0ee103fc04d916b98d75cd4bd933a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DKXGS6H25RAYNC4EGQRX2KUXQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of solitary traveling waves for generalized Hertzian chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"primary_cat":"nlin.PS","authors_text":"A. Stefanov, P.G. Kevrekidis","submitted_at":"2011-05-17T13:12:31Z","abstract_excerpt":"We consider the question of existence of \"bell-shaped\" (i.e. non-increasing for x>0 and non-decreasing for x<0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p=3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formulation of the problem. More specifically, we construct an appropriate energy functional, for which we show that the constrained minimization problem over bell-shaped entries has a solution. We also provide an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3364","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":"2026-05-18T02:01:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzyX9ROcdbccjD2TD0R4vptAaa64wQFQQ3u8zPMdCPGJ6tRT0oHbBYWrXrTPkjmsghFgNNPq/v/IAyJlSmUSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T10:39:59.008004Z"},"content_sha256":"4ea23485ddf8fffc8e3048a388d750fe27a931cd3891671a1264dd8c12c62ddc","schema_version":"1.0","event_id":"sha256:4ea23485ddf8fffc8e3048a388d750fe27a931cd3891671a1264dd8c12c62ddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/bundle.json","state_url":"https://pith.science/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/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":"2026-05-22T10:39:59Z","links":{"resolver":"https://pith.science/pith/DKXGS6H25RAYNC4EGQRX2KUXQP","bundle":"https://pith.science/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/bundle.json","state":"https://pith.science/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKXGS6H25RAYNC4EGQRX2KUXQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DKXGS6H25RAYNC4EGQRX2KUXQP","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":"e72803d1673982671efacd638d93c6d23290501550172267bc7931411e4e0509","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-05-17T13:12:31Z","title_canon_sha256":"8ec5d4b35f5af4bea94a0629a338e0e5ee095a3c649aa428869e3fbbafb1ad6b"},"schema_version":"1.0","source":{"id":"1105.3364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3364","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3364v1","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3364","created_at":"2026-05-18T02:01:57Z"},{"alias_kind":"pith_short_12","alias_value":"DKXGS6H25RAY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DKXGS6H25RAYNC4E","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DKXGS6H2","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:4ea23485ddf8fffc8e3048a388d750fe27a931cd3891671a1264dd8c12c62ddc","target":"graph","created_at":"2026-05-18T02:01:57Z","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 consider the question of existence of \"bell-shaped\" (i.e. non-increasing for x>0 and non-decreasing for x<0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p=3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formulation of the problem. More specifically, we construct an appropriate energy functional, for which we show that the constrained minimization problem over bell-shaped entries has a solution. We also provide an a","authors_text":"A. Stefanov, P.G. Kevrekidis","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-05-17T13:12:31Z","title":"On the existence of solitary traveling waves for generalized Hertzian chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3364","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":"sha256:419e4296e3e7ef8e6ab6a9a69805e77351f0ee103fc04d916b98d75cd4bd933a","target":"record","created_at":"2026-05-18T02:01:57Z","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":"e72803d1673982671efacd638d93c6d23290501550172267bc7931411e4e0509","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-05-17T13:12:31Z","title_canon_sha256":"8ec5d4b35f5af4bea94a0629a338e0e5ee095a3c649aa428869e3fbbafb1ad6b"},"schema_version":"1.0","source":{"id":"1105.3364","kind":"arxiv","version":1}},"canonical_sha256":"1aae6978faec41868b8434237d2a9783d8013937edac598b944e33d1ddfa392f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aae6978faec41868b8434237d2a9783d8013937edac598b944e33d1ddfa392f","first_computed_at":"2026-05-18T02:01:57.228882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:57.228882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fgAOPqDZFNg+/3wyT4z6WZJMxpe8o87SmbDPTtB2Z2JnjwPSfTKSv6CmMDPUlY6OnfZXHaDpMtR14vwtIebMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:57.229669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:419e4296e3e7ef8e6ab6a9a69805e77351f0ee103fc04d916b98d75cd4bd933a","sha256:4ea23485ddf8fffc8e3048a388d750fe27a931cd3891671a1264dd8c12c62ddc"],"state_sha256":"8aa0e76d4f7f97fe7b020815267556142dda5966682433507d8a7232fb3be75e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9AeY8mKYcclrSCNad+Ji7lIR6vx41mh3NCPrS6/oREVdXUy27qX1gMJJdbH5bbXjgi6TBUQqogeZlrLde+8BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T10:39:59.011790Z","bundle_sha256":"19289e07b0b99e261f3e9b17eafd3a417bad07f3795a1438d84b96dbe214c65f"}}