{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FZPRN3TN4S75W5CYPAWHFIWVSI","short_pith_number":"pith:FZPRN3TN","canonical_record":{"source":{"id":"1801.09134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-27T20:26:57Z","cross_cats_sorted":[],"title_canon_sha256":"ca2bbd10b9468b74e7d7c59d98c3852ca196338ce7caa943d99c2b21e94aef47","abstract_canon_sha256":"8b7d4116d44c4086b860a18c6e71e6de54a5738efda481eb73c81e3a684137ca"},"schema_version":"1.0"},"canonical_sha256":"2e5f16ee6de4bfdb7458782c72a2d5920163be5643a397165c081fc4558350c9","source":{"kind":"arxiv","id":"1801.09134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09134","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09134v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09134","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"FZPRN3TN4S75","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FZPRN3TN4S75W5CY","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FZPRN3TN","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FZPRN3TN4S75W5CYPAWHFIWVSI","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-27T20:26:57Z","cross_cats_sorted":[],"title_canon_sha256":"ca2bbd10b9468b74e7d7c59d98c3852ca196338ce7caa943d99c2b21e94aef47","abstract_canon_sha256":"8b7d4116d44c4086b860a18c6e71e6de54a5738efda481eb73c81e3a684137ca"},"schema_version":"1.0"},"canonical_sha256":"2e5f16ee6de4bfdb7458782c72a2d5920163be5643a397165c081fc4558350c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:58.487798Z","signature_b64":"C9Da2qamulytwJwTtleXbKnU69bx2tkkJEmpJshCmLeTGQqxjny+IUMRJDaoLV2BzLFXZZI1+JxowuBeRNoXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e5f16ee6de4bfdb7458782c72a2d5920163be5643a397165c081fc4558350c9","last_reissued_at":"2026-05-18T00:24:58.487079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:58.487079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09134","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6OZ/rn9O99SOX4R2JB6Ig8/N6sK6Cu2CIjLxYvLBca3ZVeIz/go/NYCQXXxw5hM+L3BcmgqezX18XAgXMpJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:37:01.468607Z"},"content_sha256":"62b538a8b9de3ba241b93d9943a11b2607084452a75706e0654b7fcf17ca0db0","schema_version":"1.0","event_id":"sha256:62b538a8b9de3ba241b93d9943a11b2607084452a75706e0654b7fcf17ca0db0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FZPRN3TN4S75W5CYPAWHFIWVSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behavior for the principal eigenvalue of a reinforcement problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Toshiaki Yachimura","submitted_at":"2018-01-27T20:26:57Z","abstract_excerpt":"In this paper, we consider the asymptotic behavior for the principal eigenvalue of an elliptic operator with piecewise constant coefficients. This problem was first studied by Friedman in 1980. We show how the geometric shape of the interface affects the asymptotic behavior for the principal eigenvalue. This is a refinement of the result by Friedman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09134","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGmb+TcdoAX7KK2YrJq1Stmmt/lH+wN8OHFIy1UpTKUiiWv9eCF2mN/N/r0XSn6m3J5bRH7XzdDhioTIr5D9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:37:01.468986Z"},"content_sha256":"96967a2f64b802597b7f1247feed31bf8d150b92d28f2d87b641ee4f122b80d1","schema_version":"1.0","event_id":"sha256:96967a2f64b802597b7f1247feed31bf8d150b92d28f2d87b641ee4f122b80d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/bundle.json","state_url":"https://pith.science/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/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":"2026-06-23T01:37:01Z","links":{"resolver":"https://pith.science/pith/FZPRN3TN4S75W5CYPAWHFIWVSI","bundle":"https://pith.science/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/bundle.json","state":"https://pith.science/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZPRN3TN4S75W5CYPAWHFIWVSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FZPRN3TN4S75W5CYPAWHFIWVSI","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":"8b7d4116d44c4086b860a18c6e71e6de54a5738efda481eb73c81e3a684137ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-27T20:26:57Z","title_canon_sha256":"ca2bbd10b9468b74e7d7c59d98c3852ca196338ce7caa943d99c2b21e94aef47"},"schema_version":"1.0","source":{"id":"1801.09134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09134","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09134v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09134","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"FZPRN3TN4S75","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FZPRN3TN4S75W5CY","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FZPRN3TN","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:96967a2f64b802597b7f1247feed31bf8d150b92d28f2d87b641ee4f122b80d1","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"In this paper, we consider the asymptotic behavior for the principal eigenvalue of an elliptic operator with piecewise constant coefficients. This problem was first studied by Friedman in 1980. We show how the geometric shape of the interface affects the asymptotic behavior for the principal eigenvalue. This is a refinement of the result by Friedman.","authors_text":"Toshiaki Yachimura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-27T20:26:57Z","title":"Asymptotic behavior for the principal eigenvalue of a reinforcement problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09134","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":"sha256:62b538a8b9de3ba241b93d9943a11b2607084452a75706e0654b7fcf17ca0db0","target":"record","created_at":"2026-05-18T00:24:58Z","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":"8b7d4116d44c4086b860a18c6e71e6de54a5738efda481eb73c81e3a684137ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-27T20:26:57Z","title_canon_sha256":"ca2bbd10b9468b74e7d7c59d98c3852ca196338ce7caa943d99c2b21e94aef47"},"schema_version":"1.0","source":{"id":"1801.09134","kind":"arxiv","version":1}},"canonical_sha256":"2e5f16ee6de4bfdb7458782c72a2d5920163be5643a397165c081fc4558350c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e5f16ee6de4bfdb7458782c72a2d5920163be5643a397165c081fc4558350c9","first_computed_at":"2026-05-18T00:24:58.487079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.487079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C9Da2qamulytwJwTtleXbKnU69bx2tkkJEmpJshCmLeTGQqxjny+IUMRJDaoLV2BzLFXZZI1+JxowuBeRNoXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.487798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b538a8b9de3ba241b93d9943a11b2607084452a75706e0654b7fcf17ca0db0","sha256:96967a2f64b802597b7f1247feed31bf8d150b92d28f2d87b641ee4f122b80d1"],"state_sha256":"b915f4c2fe5d84ec25b8d582e8d148f733a9418d2be385d9932a3925eb732f80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1GrkkOIWrZxju4Jlp7GRkhtglSQ4tIADiawV9R/CXHZ0xlKhLp1Akf633E2InypKLoWtWc1uvXlrdar++aLDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:37:01.470885Z","bundle_sha256":"8975ddc5e381c00ffbd26f338d5cb7270fe6852b576c807140850807c74cb30e"}}