{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4OAZVYIGP6Y4DR7Z7N5DUYXLPS","short_pith_number":"pith:4OAZVYIG","canonical_record":{"source":{"id":"1706.04044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-13T13:17:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a96eb5b96a8c58b1553b44dddca73d0b7770cd1a7e91efe4331073dea418bf0d","abstract_canon_sha256":"b9827e588fb63529c6a4a6594dcfc744ad3535f97f745d07608187ce4a00c540"},"schema_version":"1.0"},"canonical_sha256":"e3819ae1067fb1c1c7f9fb7a3a62eb7cb05dc80c0660c013d46e7c3c2c6773d6","source":{"kind":"arxiv","id":"1706.04044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04044","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04044v1","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04044","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"4OAZVYIGP6Y4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4OAZVYIGP6Y4DR7Z","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4OAZVYIG","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4OAZVYIGP6Y4DR7Z7N5DUYXLPS","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-13T13:17:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a96eb5b96a8c58b1553b44dddca73d0b7770cd1a7e91efe4331073dea418bf0d","abstract_canon_sha256":"b9827e588fb63529c6a4a6594dcfc744ad3535f97f745d07608187ce4a00c540"},"schema_version":"1.0"},"canonical_sha256":"e3819ae1067fb1c1c7f9fb7a3a62eb7cb05dc80c0660c013d46e7c3c2c6773d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:19.492766Z","signature_b64":"y0yerlpeWSksniHhPAwf+L6ycCgpxukHqeK49ttH2nNF2IBzzNhh8T26scRYm/qD3LWc1bVdAlJraIhJpVq1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3819ae1067fb1c1c7f9fb7a3a62eb7cb05dc80c0660c013d46e7c3c2c6773d6","last_reissued_at":"2026-05-18T00:42:19.492275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:19.492275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04044","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":"2026-05-18T00:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8TGAOvH4sR1PYzwPnGCEll+5HyW3/1rtJ2Vt1MZ/prsLowZs1xq3PI7xLLo/iK7Ur8cjbaNzhzbLLgt1fJ8pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:22:39.398119Z"},"content_sha256":"fd35eca4bac61542f0b94c7f3d24fde76d51b765f18a61d4355d7fe2cf815e73","schema_version":"1.0","event_id":"sha256:fd35eca4bac61542f0b94c7f3d24fde76d51b765f18a61d4355d7fe2cf815e73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4OAZVYIGP6Y4DR7Z7N5DUYXLPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some features of bending of a rod under a strong longitudinal compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"A.A. Ershov, B.I. Suleimanov","submitted_at":"2017-06-13T13:17:47Z","abstract_excerpt":"Considered typical processes of rod bending under strong longitudinal compression. The dynamic equation of bending correspponds to a perturbation of the two- dimensional Laplace equation. It is established that, for these processes, expanding of do- mains of rapid increasing of bending begins in small neighborhoods of singularity points of solutions of the limiting Laplace's equation. The initial stages of these increases are described using the Hardy integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04044","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":"2026-05-18T00:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apgT0bxPYxbCxsXM0MaWBJjgvI51KtxtMgu9M8YoATDYCMY9x5kFEebL0j78ZvE1kf5SgwNsas+xlsfd5eWXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:22:39.398478Z"},"content_sha256":"240742016ab4db31088b24b1c03bd6a009b26cf7106b62d7344932c1ca227c21","schema_version":"1.0","event_id":"sha256:240742016ab4db31088b24b1c03bd6a009b26cf7106b62d7344932c1ca227c21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/bundle.json","state_url":"https://pith.science/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/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":"2026-06-29T17:22:39Z","links":{"resolver":"https://pith.science/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS","bundle":"https://pith.science/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/bundle.json","state":"https://pith.science/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4OAZVYIGP6Y4DR7Z7N5DUYXLPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4OAZVYIGP6Y4DR7Z7N5DUYXLPS","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":"b9827e588fb63529c6a4a6594dcfc744ad3535f97f745d07608187ce4a00c540","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-13T13:17:47Z","title_canon_sha256":"a96eb5b96a8c58b1553b44dddca73d0b7770cd1a7e91efe4331073dea418bf0d"},"schema_version":"1.0","source":{"id":"1706.04044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04044","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04044v1","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04044","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"4OAZVYIGP6Y4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4OAZVYIGP6Y4DR7Z","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4OAZVYIG","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:240742016ab4db31088b24b1c03bd6a009b26cf7106b62d7344932c1ca227c21","target":"graph","created_at":"2026-05-18T00:42:19Z","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":"Considered typical processes of rod bending under strong longitudinal compression. The dynamic equation of bending correspponds to a perturbation of the two- dimensional Laplace equation. It is established that, for these processes, expanding of do- mains of rapid increasing of bending begins in small neighborhoods of singularity points of solutions of the limiting Laplace's equation. The initial stages of these increases are described using the Hardy integral.","authors_text":"A.A. Ershov, B.I. Suleimanov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-13T13:17:47Z","title":"Some features of bending of a rod under a strong longitudinal compression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04044","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:fd35eca4bac61542f0b94c7f3d24fde76d51b765f18a61d4355d7fe2cf815e73","target":"record","created_at":"2026-05-18T00:42:19Z","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":"b9827e588fb63529c6a4a6594dcfc744ad3535f97f745d07608187ce4a00c540","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-13T13:17:47Z","title_canon_sha256":"a96eb5b96a8c58b1553b44dddca73d0b7770cd1a7e91efe4331073dea418bf0d"},"schema_version":"1.0","source":{"id":"1706.04044","kind":"arxiv","version":1}},"canonical_sha256":"e3819ae1067fb1c1c7f9fb7a3a62eb7cb05dc80c0660c013d46e7c3c2c6773d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3819ae1067fb1c1c7f9fb7a3a62eb7cb05dc80c0660c013d46e7c3c2c6773d6","first_computed_at":"2026-05-18T00:42:19.492275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:19.492275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y0yerlpeWSksniHhPAwf+L6ycCgpxukHqeK49ttH2nNF2IBzzNhh8T26scRYm/qD3LWc1bVdAlJraIhJpVq1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:19.492766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd35eca4bac61542f0b94c7f3d24fde76d51b765f18a61d4355d7fe2cf815e73","sha256:240742016ab4db31088b24b1c03bd6a009b26cf7106b62d7344932c1ca227c21"],"state_sha256":"a6dd0fe120d165555060212da14ccae3a216c0542d363cb58a9b11e4beac1e08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOv6rumkQ5MnQHfblyWgBqWMQptKClYzu6FyF+PurX7jFtwB5y0HfQG5iLXmskhozv7L7gAx2XXh7bqSznxtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T17:22:39.400471Z","bundle_sha256":"1270a1183aff80546970a7f2d0b768465d12957d09aed08e65cbfdc6111e7aa4"}}