{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PETPEPM5I5QPO53TOGSIA24CDZ","short_pith_number":"pith:PETPEPM5","canonical_record":{"source":{"id":"1102.4199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-21T11:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"32b093744db03e77d18151aa27c4fe69a58d0000aaa95daa995b2d5cd5b7567e","abstract_canon_sha256":"a736de76c019af698c2d694ff6458a1e3e83e79637ee240af4496f8414ddd07b"},"schema_version":"1.0"},"canonical_sha256":"7926f23d9d4760f7777371a4806b821e552b1032b5c3553e0c00603711248cd5","source":{"kind":"arxiv","id":"1102.4199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4199","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4199v2","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4199","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"PETPEPM5I5QP","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PETPEPM5I5QPO53T","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PETPEPM5","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PETPEPM5I5QPO53TOGSIA24CDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-21T11:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"32b093744db03e77d18151aa27c4fe69a58d0000aaa95daa995b2d5cd5b7567e","abstract_canon_sha256":"a736de76c019af698c2d694ff6458a1e3e83e79637ee240af4496f8414ddd07b"},"schema_version":"1.0"},"canonical_sha256":"7926f23d9d4760f7777371a4806b821e552b1032b5c3553e0c00603711248cd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:38.798718Z","signature_b64":"sXoFHVLRkMa0KXBUiLsoxzzinsJv3f/l5SeUUYQuLMH7Hm64IRwFDAcxJgIdvte7dKYQ4vD4fkDzcI9fln7wBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7926f23d9d4760f7777371a4806b821e552b1032b5c3553e0c00603711248cd5","last_reissued_at":"2026-05-18T04:25:38.798224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:38.798224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4199","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yBYj0TKyDIOefIho66Yk1v6ly+tptGBy1/fN2BdK+byt8o4uF7UrergUE4nz3sYSqJ+EFGS0jRKl2pOy7kQhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:29:24.083003Z"},"content_sha256":"e247be69ded42f155fa0134805c4181b9a87da4e7b871824dff25a8332e85fe0","schema_version":"1.0","event_id":"sha256:e247be69ded42f155fa0134805c4181b9a87da4e7b871824dff25a8332e85fe0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PETPEPM5I5QPO53TOGSIA24CDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Neumann problem for Sturm-Liouville equation with self-similar Cantor type weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A. A. Vladimirov, I. A. Sheipak","submitted_at":"2011-02-21T11:57:07Z","abstract_excerpt":"Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral asymptotics are made more precise then in previous papers. Namely, it is shown that for known asymptotics $N(\\lambda)=\\lambda^D\\cdot [s(\\ln\\lambda)+o(1)]$ the function $s$ is a product of decreasing exponent and nondecreasing purely singular function (and hence it is not constant)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4199","kind":"arxiv","version":2},"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":"2026-05-18T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s0IkoVfUmrFU0PmIFV7kJn81MIe9FwrRed72wFkVqkZ2w9aZ3iBN34IEEsWyYyJSG3Lp2H9cD8T3uyald+MYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:29:24.083349Z"},"content_sha256":"4d320c6528ea40ef738c800dc66c39d6812dd11e8af512b15a67fc57a441d70d","schema_version":"1.0","event_id":"sha256:4d320c6528ea40ef738c800dc66c39d6812dd11e8af512b15a67fc57a441d70d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PETPEPM5I5QPO53TOGSIA24CDZ/bundle.json","state_url":"https://pith.science/pith/PETPEPM5I5QPO53TOGSIA24CDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PETPEPM5I5QPO53TOGSIA24CDZ/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":"2026-07-06T14:29:24Z","links":{"resolver":"https://pith.science/pith/PETPEPM5I5QPO53TOGSIA24CDZ","bundle":"https://pith.science/pith/PETPEPM5I5QPO53TOGSIA24CDZ/bundle.json","state":"https://pith.science/pith/PETPEPM5I5QPO53TOGSIA24CDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PETPEPM5I5QPO53TOGSIA24CDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PETPEPM5I5QPO53TOGSIA24CDZ","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":"a736de76c019af698c2d694ff6458a1e3e83e79637ee240af4496f8414ddd07b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-21T11:57:07Z","title_canon_sha256":"32b093744db03e77d18151aa27c4fe69a58d0000aaa95daa995b2d5cd5b7567e"},"schema_version":"1.0","source":{"id":"1102.4199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4199","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4199v2","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4199","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"PETPEPM5I5QP","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PETPEPM5I5QPO53T","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PETPEPM5","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:4d320c6528ea40ef738c800dc66c39d6812dd11e8af512b15a67fc57a441d70d","target":"graph","created_at":"2026-05-18T04:25:38Z","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":"Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral asymptotics are made more precise then in previous papers. Namely, it is shown that for known asymptotics $N(\\lambda)=\\lambda^D\\cdot [s(\\ln\\lambda)+o(1)]$ the function $s$ is a product of decreasing exponent and nondecreasing purely singular function (and hence it is not constant).","authors_text":"A. A. Vladimirov, I. A. Sheipak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-21T11:57:07Z","title":"On the Neumann problem for Sturm-Liouville equation with self-similar Cantor type weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4199","kind":"arxiv","version":2},"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:e247be69ded42f155fa0134805c4181b9a87da4e7b871824dff25a8332e85fe0","target":"record","created_at":"2026-05-18T04:25:38Z","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":"a736de76c019af698c2d694ff6458a1e3e83e79637ee240af4496f8414ddd07b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-21T11:57:07Z","title_canon_sha256":"32b093744db03e77d18151aa27c4fe69a58d0000aaa95daa995b2d5cd5b7567e"},"schema_version":"1.0","source":{"id":"1102.4199","kind":"arxiv","version":2}},"canonical_sha256":"7926f23d9d4760f7777371a4806b821e552b1032b5c3553e0c00603711248cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7926f23d9d4760f7777371a4806b821e552b1032b5c3553e0c00603711248cd5","first_computed_at":"2026-05-18T04:25:38.798224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:38.798224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sXoFHVLRkMa0KXBUiLsoxzzinsJv3f/l5SeUUYQuLMH7Hm64IRwFDAcxJgIdvte7dKYQ4vD4fkDzcI9fln7wBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:38.798718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e247be69ded42f155fa0134805c4181b9a87da4e7b871824dff25a8332e85fe0","sha256:4d320c6528ea40ef738c800dc66c39d6812dd11e8af512b15a67fc57a441d70d"],"state_sha256":"0badc7464613b3e52906ef13ef4833671b01c36475b69d5ccb205c2f1bb59544"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHh/pk7Bz48IxOhQ1RNEQs6uJ3dDzm7TO810gzTGxJWmcOZSy+haq91OJA73vAHKJssEI4i7lZF4mepzSMBHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:29:24.085090Z","bundle_sha256":"732be52bfa5c62542ecd46ebaf08057861b603788ff453627baa3e48ca8e6e5b"}}