{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5SNA5S34IMIOMGO444PNCGAYT7","short_pith_number":"pith:5SNA5S34","canonical_record":{"source":{"id":"1103.1826","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-09T16:41:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aff34904e30c223c40a1f989ecd2e67fb7fe3884ca94258f0fcf6a1989fe3022","abstract_canon_sha256":"b71a6e8b00a4ec51fbd42bd140db184807c2683a1570cc9b838b7b414dc444ae"},"schema_version":"1.0"},"canonical_sha256":"ec9a0ecb7c4310e619dce71ed118189fd661290409c369fc97d0aff658bc5823","source":{"kind":"arxiv","id":"1103.1826","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1826","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1826v3","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1826","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"5SNA5S34IMIO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5SNA5S34IMIOMGO4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5SNA5S34","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5SNA5S34IMIOMGO444PNCGAYT7","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1826","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-09T16:41:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aff34904e30c223c40a1f989ecd2e67fb7fe3884ca94258f0fcf6a1989fe3022","abstract_canon_sha256":"b71a6e8b00a4ec51fbd42bd140db184807c2683a1570cc9b838b7b414dc444ae"},"schema_version":"1.0"},"canonical_sha256":"ec9a0ecb7c4310e619dce71ed118189fd661290409c369fc97d0aff658bc5823","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:56.512298Z","signature_b64":"TynX0NFIEolDYbsfb3+fWoLLoCUA26hGbCJvtcoHzPld3vxrKUkPNUFJlm+FVuBFjYmNjnYKT8VKLyVohD7ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec9a0ecb7c4310e619dce71ed118189fd661290409c369fc97d0aff658bc5823","last_reissued_at":"2026-05-18T03:28:56.511508Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:56.511508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1826","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":"2026-05-18T03:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LU7JXJ45dtCzlGVt1jHXgYuh6gvnd/myS6Myn8TFHxlyyFuwGnXaCBsJs9ax6ub/F7S4IK0loh+SXMoOJsOTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:15:25.794835Z"},"content_sha256":"b69cb696b8c029203478ffd2e9a35fccf02ddd81e3d0f2e8a616a040fd3e87a2","schema_version":"1.0","event_id":"sha256:b69cb696b8c029203478ffd2e9a35fccf02ddd81e3d0f2e8a616a040fd3e87a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5SNA5S34IMIOMGO444PNCGAYT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The conformal Yamabe constant of product manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","submitted_at":"2011-03-09T16:41:10Z","abstract_excerpt":"Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1826","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":"2026-05-18T03:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dPlN0kQCGxOyXmiStDykyFpJ1CnTlZjRgQqSRafjnT7kHhEse0XbpU7PteZDU3yXJnq7lEPXc7xwuQGCCvQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:15:25.795173Z"},"content_sha256":"126a0219476e63d0b732c4812dfeae36c30c7c6ebe31295647993836326c59fe","schema_version":"1.0","event_id":"sha256:126a0219476e63d0b732c4812dfeae36c30c7c6ebe31295647993836326c59fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SNA5S34IMIOMGO444PNCGAYT7/bundle.json","state_url":"https://pith.science/pith/5SNA5S34IMIOMGO444PNCGAYT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SNA5S34IMIOMGO444PNCGAYT7/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":"2026-05-28T08:15:25Z","links":{"resolver":"https://pith.science/pith/5SNA5S34IMIOMGO444PNCGAYT7","bundle":"https://pith.science/pith/5SNA5S34IMIOMGO444PNCGAYT7/bundle.json","state":"https://pith.science/pith/5SNA5S34IMIOMGO444PNCGAYT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SNA5S34IMIOMGO444PNCGAYT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5SNA5S34IMIOMGO444PNCGAYT7","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":"b71a6e8b00a4ec51fbd42bd140db184807c2683a1570cc9b838b7b414dc444ae","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-09T16:41:10Z","title_canon_sha256":"aff34904e30c223c40a1f989ecd2e67fb7fe3884ca94258f0fcf6a1989fe3022"},"schema_version":"1.0","source":{"id":"1103.1826","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1826","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1826v3","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1826","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"5SNA5S34IMIO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5SNA5S34IMIOMGO4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5SNA5S34","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:126a0219476e63d0b732c4812dfeae36c30c7c6ebe31295647993836326c59fe","target":"graph","created_at":"2026-05-18T03:28:56Z","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":"Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-09T16:41:10Z","title":"The conformal Yamabe constant of product manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1826","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:b69cb696b8c029203478ffd2e9a35fccf02ddd81e3d0f2e8a616a040fd3e87a2","target":"record","created_at":"2026-05-18T03:28:56Z","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":"b71a6e8b00a4ec51fbd42bd140db184807c2683a1570cc9b838b7b414dc444ae","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-09T16:41:10Z","title_canon_sha256":"aff34904e30c223c40a1f989ecd2e67fb7fe3884ca94258f0fcf6a1989fe3022"},"schema_version":"1.0","source":{"id":"1103.1826","kind":"arxiv","version":3}},"canonical_sha256":"ec9a0ecb7c4310e619dce71ed118189fd661290409c369fc97d0aff658bc5823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec9a0ecb7c4310e619dce71ed118189fd661290409c369fc97d0aff658bc5823","first_computed_at":"2026-05-18T03:28:56.511508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:56.511508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TynX0NFIEolDYbsfb3+fWoLLoCUA26hGbCJvtcoHzPld3vxrKUkPNUFJlm+FVuBFjYmNjnYKT8VKLyVohD7ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:56.512298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1826","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b69cb696b8c029203478ffd2e9a35fccf02ddd81e3d0f2e8a616a040fd3e87a2","sha256:126a0219476e63d0b732c4812dfeae36c30c7c6ebe31295647993836326c59fe"],"state_sha256":"c506dc8734cdaf273b29c8896e12c5dd6c4fad544c7302f23c09bb7e436be836"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtcD7n2YsL04ZTVw9CFdVBu+XaOtAEeUYP9EnzlcoiQxMLKPFsauo7dQZW/+r7PSj7Z6JbugzQhaxUu/ky/FAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:15:25.797166Z","bundle_sha256":"f1d7d8eaa8e55f4a800758a920bf42f5645a71a869b5b4d8d3c71c4838a11dd7"}}