{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KZOGJM5AC6CVQVCWJC2ZBUGV7L","short_pith_number":"pith:KZOGJM5A","canonical_record":{"source":{"id":"1604.06888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T10:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"8c2393ab992200519db4558fed956c9d48f06dbf2683f04f1e7d031e998c6cc2","abstract_canon_sha256":"c77218ae66baa2974fbdab0854db722838f070e314d1dd870cc6e00ec2d93cc5"},"schema_version":"1.0"},"canonical_sha256":"565c64b3a0178558545648b590d0d5fae43877f3659187aa56492eb707caed83","source":{"kind":"arxiv","id":"1604.06888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06888","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06888v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06888","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"KZOGJM5AC6CV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KZOGJM5AC6CVQVCW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KZOGJM5A","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KZOGJM5AC6CVQVCWJC2ZBUGV7L","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T10:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"8c2393ab992200519db4558fed956c9d48f06dbf2683f04f1e7d031e998c6cc2","abstract_canon_sha256":"c77218ae66baa2974fbdab0854db722838f070e314d1dd870cc6e00ec2d93cc5"},"schema_version":"1.0"},"canonical_sha256":"565c64b3a0178558545648b590d0d5fae43877f3659187aa56492eb707caed83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:23.685247Z","signature_b64":"0WkZTQLLuNxPGeIwUs1enqaf6ADnl7s/uTQ1/2ASOdBo87+Ea31pOwmoiNiQ7Srer8NmGk4IhnybXMwuxMadAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"565c64b3a0178558545648b590d0d5fae43877f3659187aa56492eb707caed83","last_reissued_at":"2026-05-18T01:16:23.684544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:23.684544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06888","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":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLsTvjZfx78i1skm0YrNCS8NiKSExgN/pdytSWiYY5q4dB45IRkiezkaRENmopLSMM+acplkiC9+yvIFXaQTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:26:00.060619Z"},"content_sha256":"73962f8efbd9b91e7764e106f800813bff430a3d972262d214906c184268a1c3","schema_version":"1.0","event_id":"sha256:73962f8efbd9b91e7764e106f800813bff430a3d972262d214906c184268a1c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KZOGJM5AC6CVQVCWJC2ZBUGV7L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral homogenization for a Robin-Neumann problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Cancedda","submitted_at":"2016-04-23T10:10:43Z","abstract_excerpt":"We consider a Neumann-Robin spectral problem in a perforated domain $\\Omeps$. By homogenization techniques we find the suitable homogenized problem and we discuss the asymptotics of eigenpairs, as the size of the perforation tends to zero. Our results involve an approach based on Vi\\v{s}\\'ik lemma and the Mosco convergence of eigenspaces. We prove that eigenpairs of our problem converge to eigenpairs of the homogenized problem with rate $\\sqrt{\\eps}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06888","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":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GsbD7hc9Z73tc9yoGYvnrZQdO23NFlVNeMiggFF6ibfXsrYbmDMZTYiIKjNe9XCvg49T+HulJ5VYYwRljk2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:26:00.061233Z"},"content_sha256":"f370f9abe487f040d01da420eb3c1de5e00ef0bd119f3a70c9f4e225346c0340","schema_version":"1.0","event_id":"sha256:f370f9abe487f040d01da420eb3c1de5e00ef0bd119f3a70c9f4e225346c0340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/bundle.json","state_url":"https://pith.science/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/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":"2026-06-12T03:26:00Z","links":{"resolver":"https://pith.science/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L","bundle":"https://pith.science/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/bundle.json","state":"https://pith.science/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZOGJM5AC6CVQVCWJC2ZBUGV7L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KZOGJM5AC6CVQVCWJC2ZBUGV7L","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":"c77218ae66baa2974fbdab0854db722838f070e314d1dd870cc6e00ec2d93cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T10:10:43Z","title_canon_sha256":"8c2393ab992200519db4558fed956c9d48f06dbf2683f04f1e7d031e998c6cc2"},"schema_version":"1.0","source":{"id":"1604.06888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06888","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06888v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06888","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"KZOGJM5AC6CV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KZOGJM5AC6CVQVCW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KZOGJM5A","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:f370f9abe487f040d01da420eb3c1de5e00ef0bd119f3a70c9f4e225346c0340","target":"graph","created_at":"2026-05-18T01:16:23Z","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 a Neumann-Robin spectral problem in a perforated domain $\\Omeps$. By homogenization techniques we find the suitable homogenized problem and we discuss the asymptotics of eigenpairs, as the size of the perforation tends to zero. Our results involve an approach based on Vi\\v{s}\\'ik lemma and the Mosco convergence of eigenspaces. We prove that eigenpairs of our problem converge to eigenpairs of the homogenized problem with rate $\\sqrt{\\eps}$.","authors_text":"Andrea Cancedda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T10:10:43Z","title":"Spectral homogenization for a Robin-Neumann problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06888","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":"sha256:73962f8efbd9b91e7764e106f800813bff430a3d972262d214906c184268a1c3","target":"record","created_at":"2026-05-18T01:16:23Z","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":"c77218ae66baa2974fbdab0854db722838f070e314d1dd870cc6e00ec2d93cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T10:10:43Z","title_canon_sha256":"8c2393ab992200519db4558fed956c9d48f06dbf2683f04f1e7d031e998c6cc2"},"schema_version":"1.0","source":{"id":"1604.06888","kind":"arxiv","version":1}},"canonical_sha256":"565c64b3a0178558545648b590d0d5fae43877f3659187aa56492eb707caed83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"565c64b3a0178558545648b590d0d5fae43877f3659187aa56492eb707caed83","first_computed_at":"2026-05-18T01:16:23.684544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:23.684544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0WkZTQLLuNxPGeIwUs1enqaf6ADnl7s/uTQ1/2ASOdBo87+Ea31pOwmoiNiQ7Srer8NmGk4IhnybXMwuxMadAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:23.685247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73962f8efbd9b91e7764e106f800813bff430a3d972262d214906c184268a1c3","sha256:f370f9abe487f040d01da420eb3c1de5e00ef0bd119f3a70c9f4e225346c0340"],"state_sha256":"96f28774c2837f42071a3733641770e7598d04681e3e3718cafa8a6fab6cfc06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGV9gbIQPvA+YTq45K9nywDuFiZqwwr4CMjCBTvz9fd8gGG6IkrTMqLr/NtYHkODmaimBPx3LevN8grJOOB0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:26:00.065767Z","bundle_sha256":"f2ef17624ad888d378b3b5a2710ea1e80c89228bfb43d2f3348ef60d71d57d76"}}