{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SD2R2U5EQF2OITPN4NUQ7JSDRX","short_pith_number":"pith:SD2R2U5E","canonical_record":{"source":{"id":"1301.7150","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-30T06:11:06Z","cross_cats_sorted":[],"title_canon_sha256":"f86f176721b3df2115fe1e9eca36091a4bc93c060f4612ad80c1b3f7ed9799a1","abstract_canon_sha256":"873e2b755e2e83a2707b42c36ef08ef644ef14f98b1683299451dfd83e380ce9"},"schema_version":"1.0"},"canonical_sha256":"90f51d53a48174e44dede3690fa6438dd27bc0f0803d9646b3f73568fe4c40b0","source":{"kind":"arxiv","id":"1301.7150","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7150","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7150v3","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7150","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"SD2R2U5EQF2O","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SD2R2U5EQF2OITPN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SD2R2U5E","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SD2R2U5EQF2OITPN4NUQ7JSDRX","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7150","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-30T06:11:06Z","cross_cats_sorted":[],"title_canon_sha256":"f86f176721b3df2115fe1e9eca36091a4bc93c060f4612ad80c1b3f7ed9799a1","abstract_canon_sha256":"873e2b755e2e83a2707b42c36ef08ef644ef14f98b1683299451dfd83e380ce9"},"schema_version":"1.0"},"canonical_sha256":"90f51d53a48174e44dede3690fa6438dd27bc0f0803d9646b3f73568fe4c40b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:27.612772Z","signature_b64":"vlpGMxABhD9IkhhgHcgw/DXXXmIt/TuyXK1+dR2Y/l3P90yqnO1dSdUiuQKcnol328UYxc8BKt+ralVbPMXwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f51d53a48174e44dede3690fa6438dd27bc0f0803d9646b3f73568fe4c40b0","last_reissued_at":"2026-05-18T02:31:27.612275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:27.612275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7150","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnO77dm6/S0xyw3O5rt2v0UF0z0w+Lpp/H3OxHPvM+fkaSm+5640VGLSIIbzYn1uCoxKH+GlmWLt8SA0eoFtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:43:11.131969Z"},"content_sha256":"1e1e86b8d4e5106b630489b720a7fff4ef7e9a23e3e702762262487d127e3d85","schema_version":"1.0","event_id":"sha256:1e1e86b8d4e5106b630489b720a7fff4ef7e9a23e3e702762262487d127e3d85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SD2R2U5EQF2OITPN4NUQ7JSDRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal change of Riemannian metrics and biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hajime Urakawa, Hisashi Naito","submitted_at":"2013-01-30T06:11:06Z","abstract_excerpt":"For the reduction ordinary differential equation due to Baird and Kamissoko \\cite{BK} for biharmonic maps from a Riemannian manifold $(M^m,g)$ into another one $(N^n,h)$, we show that this ODE has no global positive solution for every $m\\geq 5$. On the contrary, we show that there exist global positive solutions in the case $m=3$. As applications, for the the Riemannian product $(M^3,g)$ of the line and a Riemann surface, we construct the new metric $\\widetilde{g}$ on $M^3$ conformal to $g$ such that every nontrivial product harmonic map from $M^3$ with respect to the original metric $g$ must "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7150","kind":"arxiv","version":3},"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":"2026-05-18T02:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2N5tXJgQ8x+fIN3G4VC/uZR0Mj2CxQKT+Yb0u+AgYcmnT1p5pzcWDNta0ap7algbPbIlV33M3RDhuxVA1vGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:43:11.132375Z"},"content_sha256":"91aeb2b6e8cd093947e1c6aab120406c3e4c376c5e3fc3baf17b66cd35117a63","schema_version":"1.0","event_id":"sha256:91aeb2b6e8cd093947e1c6aab120406c3e4c376c5e3fc3baf17b66cd35117a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/bundle.json","state_url":"https://pith.science/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/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":"2026-06-04T02:43:11Z","links":{"resolver":"https://pith.science/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX","bundle":"https://pith.science/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/bundle.json","state":"https://pith.science/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SD2R2U5EQF2OITPN4NUQ7JSDRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SD2R2U5EQF2OITPN4NUQ7JSDRX","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":"873e2b755e2e83a2707b42c36ef08ef644ef14f98b1683299451dfd83e380ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-30T06:11:06Z","title_canon_sha256":"f86f176721b3df2115fe1e9eca36091a4bc93c060f4612ad80c1b3f7ed9799a1"},"schema_version":"1.0","source":{"id":"1301.7150","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7150","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7150v3","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7150","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"SD2R2U5EQF2O","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SD2R2U5EQF2OITPN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SD2R2U5E","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:91aeb2b6e8cd093947e1c6aab120406c3e4c376c5e3fc3baf17b66cd35117a63","target":"graph","created_at":"2026-05-18T02:31:27Z","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":"For the reduction ordinary differential equation due to Baird and Kamissoko \\cite{BK} for biharmonic maps from a Riemannian manifold $(M^m,g)$ into another one $(N^n,h)$, we show that this ODE has no global positive solution for every $m\\geq 5$. On the contrary, we show that there exist global positive solutions in the case $m=3$. As applications, for the the Riemannian product $(M^3,g)$ of the line and a Riemann surface, we construct the new metric $\\widetilde{g}$ on $M^3$ conformal to $g$ such that every nontrivial product harmonic map from $M^3$ with respect to the original metric $g$ must ","authors_text":"Hajime Urakawa, Hisashi Naito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-30T06:11:06Z","title":"Conformal change of Riemannian metrics and biharmonic maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7150","kind":"arxiv","version":3},"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":"sha256:1e1e86b8d4e5106b630489b720a7fff4ef7e9a23e3e702762262487d127e3d85","target":"record","created_at":"2026-05-18T02:31:27Z","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":"873e2b755e2e83a2707b42c36ef08ef644ef14f98b1683299451dfd83e380ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-30T06:11:06Z","title_canon_sha256":"f86f176721b3df2115fe1e9eca36091a4bc93c060f4612ad80c1b3f7ed9799a1"},"schema_version":"1.0","source":{"id":"1301.7150","kind":"arxiv","version":3}},"canonical_sha256":"90f51d53a48174e44dede3690fa6438dd27bc0f0803d9646b3f73568fe4c40b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f51d53a48174e44dede3690fa6438dd27bc0f0803d9646b3f73568fe4c40b0","first_computed_at":"2026-05-18T02:31:27.612275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:27.612275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vlpGMxABhD9IkhhgHcgw/DXXXmIt/TuyXK1+dR2Y/l3P90yqnO1dSdUiuQKcnol328UYxc8BKt+ralVbPMXwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:27.612772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7150","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e1e86b8d4e5106b630489b720a7fff4ef7e9a23e3e702762262487d127e3d85","sha256:91aeb2b6e8cd093947e1c6aab120406c3e4c376c5e3fc3baf17b66cd35117a63"],"state_sha256":"f18cc4d71431c1d58236c8f02062b7302ea17610ca873c72ffb6e93e390e37d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ILY6Ubfz+jIV5MXWeGQGjfU0Z1zJa4HT3BAXuLP0/e09/WZusgnnZ56YBxdww7SikcQivemJOu8gB7kO9GAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:43:11.134630Z","bundle_sha256":"2eb7138f9159eb4fa594e126c4497e3de8d0505e16a41db4e13a8c57bfc1e7d7"}}