{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZZUBWCKTMN2TF453RFUXSIOHQV","short_pith_number":"pith:ZZUBWCKT","canonical_record":{"source":{"id":"0912.5224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-12-28T23:09:13Z","cross_cats_sorted":[],"title_canon_sha256":"f11c2a574f8d3b065aad547bb9f610ed46cbe86d36f9dcfe70330fb9bde7a30e","abstract_canon_sha256":"5e87822e5e569bfbe6f9f220b49a058a8d2d0c45cc4686d25fc3a79453cb523a"},"schema_version":"1.0"},"canonical_sha256":"ce681b0953637532f3bb89697921c785606ea2b8da2d321061c8f25c30d1385f","source":{"kind":"arxiv","id":"0912.5224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.5224","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"0912.5224v1","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.5224","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZZUBWCKTMN2T","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZZUBWCKTMN2TF453","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZZUBWCKT","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZZUBWCKTMN2TF453RFUXSIOHQV","target":"record","payload":{"canonical_record":{"source":{"id":"0912.5224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-12-28T23:09:13Z","cross_cats_sorted":[],"title_canon_sha256":"f11c2a574f8d3b065aad547bb9f610ed46cbe86d36f9dcfe70330fb9bde7a30e","abstract_canon_sha256":"5e87822e5e569bfbe6f9f220b49a058a8d2d0c45cc4686d25fc3a79453cb523a"},"schema_version":"1.0"},"canonical_sha256":"ce681b0953637532f3bb89697921c785606ea2b8da2d321061c8f25c30d1385f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:05.562451Z","signature_b64":"WXWgG9exU4QOx+mfssIPRs0s3nuNpAI6FPGSXM/IeHNb5h8TUplk7TT/x2p+y73SPihAZBkAF4/lYw2ghdonDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce681b0953637532f3bb89697921c785606ea2b8da2d321061c8f25c30d1385f","last_reissued_at":"2026-05-18T03:39:05.561811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:05.561811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.5224","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":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODMFXh4SLrnfNDzLl2FXUMGEOM5TBxHK7MPCqHDUkFDqkNE/b+NJ+15M7YF0RAPVCnev7ZmOuyTFTWe8k28uDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:14:54.582840Z"},"content_sha256":"7fbfdd14bce2cf90ed5e208d585132daf935c9fb9b290f966cc3ef185fc2d91c","schema_version":"1.0","event_id":"sha256:7fbfdd14bce2cf90ed5e208d585132daf935c9fb9b290f966cc3ef185fc2d91c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZZUBWCKTMN2TF453RFUXSIOHQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dependence on parameters for discrete second order boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Marek Galewski","submitted_at":"2009-12-28T23:09:13Z","abstract_excerpt":"We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications for discrete Emden-Fowler equation are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5224","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":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QckP22bJRB5v9E9yTolsROjuxbONWIblCqDjS7phSdqqiEUZc1mh8WG1wNdS2LcL+ln66Gfh4ScJxWcSm4BmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:14:54.583183Z"},"content_sha256":"6d1219f1de52b063a0623056f0b27956775692672ac77b67998e3e59034a2f8c","schema_version":"1.0","event_id":"sha256:6d1219f1de52b063a0623056f0b27956775692672ac77b67998e3e59034a2f8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/bundle.json","state_url":"https://pith.science/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/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":"2026-06-03T18:14:54Z","links":{"resolver":"https://pith.science/pith/ZZUBWCKTMN2TF453RFUXSIOHQV","bundle":"https://pith.science/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/bundle.json","state":"https://pith.science/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZUBWCKTMN2TF453RFUXSIOHQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZZUBWCKTMN2TF453RFUXSIOHQV","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":"5e87822e5e569bfbe6f9f220b49a058a8d2d0c45cc4686d25fc3a79453cb523a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-12-28T23:09:13Z","title_canon_sha256":"f11c2a574f8d3b065aad547bb9f610ed46cbe86d36f9dcfe70330fb9bde7a30e"},"schema_version":"1.0","source":{"id":"0912.5224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.5224","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"0912.5224v1","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.5224","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZZUBWCKTMN2T","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZZUBWCKTMN2TF453","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZZUBWCKT","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:6d1219f1de52b063a0623056f0b27956775692672ac77b67998e3e59034a2f8c","target":"graph","created_at":"2026-05-18T03:39:05Z","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 investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications for discrete Emden-Fowler equation are also given.","authors_text":"Marek Galewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-12-28T23:09:13Z","title":"Dependence on parameters for discrete second order boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5224","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":"sha256:7fbfdd14bce2cf90ed5e208d585132daf935c9fb9b290f966cc3ef185fc2d91c","target":"record","created_at":"2026-05-18T03:39:05Z","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":"5e87822e5e569bfbe6f9f220b49a058a8d2d0c45cc4686d25fc3a79453cb523a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-12-28T23:09:13Z","title_canon_sha256":"f11c2a574f8d3b065aad547bb9f610ed46cbe86d36f9dcfe70330fb9bde7a30e"},"schema_version":"1.0","source":{"id":"0912.5224","kind":"arxiv","version":1}},"canonical_sha256":"ce681b0953637532f3bb89697921c785606ea2b8da2d321061c8f25c30d1385f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce681b0953637532f3bb89697921c785606ea2b8da2d321061c8f25c30d1385f","first_computed_at":"2026-05-18T03:39:05.561811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:05.561811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXWgG9exU4QOx+mfssIPRs0s3nuNpAI6FPGSXM/IeHNb5h8TUplk7TT/x2p+y73SPihAZBkAF4/lYw2ghdonDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:05.562451Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.5224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fbfdd14bce2cf90ed5e208d585132daf935c9fb9b290f966cc3ef185fc2d91c","sha256:6d1219f1de52b063a0623056f0b27956775692672ac77b67998e3e59034a2f8c"],"state_sha256":"48a74eecd34706713c89d5e10c81f6ee5c3aec3e13649cea3f65bd628475732d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nPNEnlP0iheNHqjnozBNKrEFMsO8Ry68Lq58NRr33aBb9Zn4tGYXIbwXRPVPWTL3hNLoJjX26FQYbCQVA2YHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:14:54.585065Z","bundle_sha256":"ee714d592163b09b52d911cb5dc4dec769989d3becf18b2bb23b039404707927"}}