{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SOVMJWWDMUSFZ7EPLGAEEXM65N","short_pith_number":"pith:SOVMJWWD","canonical_record":{"source":{"id":"1508.02727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-11T20:13:23Z","cross_cats_sorted":[],"title_canon_sha256":"3d560ac436d4a76e5f659caad7b1e3ddce1fb7173b4b88e0329882da69a49b95","abstract_canon_sha256":"faad34e449a869411323dfa2917d976fc9cc76cf0c6fd4c6439514082ee0c408"},"schema_version":"1.0"},"canonical_sha256":"93aac4dac365245cfc8f5980425d9eeb714696915b989f58f871aeb26381588d","source":{"kind":"arxiv","id":"1508.02727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02727","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02727v1","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02727","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"SOVMJWWDMUSF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOVMJWWDMUSFZ7EP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOVMJWWD","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SOVMJWWDMUSFZ7EPLGAEEXM65N","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-11T20:13:23Z","cross_cats_sorted":[],"title_canon_sha256":"3d560ac436d4a76e5f659caad7b1e3ddce1fb7173b4b88e0329882da69a49b95","abstract_canon_sha256":"faad34e449a869411323dfa2917d976fc9cc76cf0c6fd4c6439514082ee0c408"},"schema_version":"1.0"},"canonical_sha256":"93aac4dac365245cfc8f5980425d9eeb714696915b989f58f871aeb26381588d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:26.332826Z","signature_b64":"xQPnMHJVn3qR2Qh+Ixzo9U0L4JrC8lBbr/Gt7njBPmUj6UEkXWvjcgI9fctT9u0PWbtMpRAtlbAiz4rN0w3IBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93aac4dac365245cfc8f5980425d9eeb714696915b989f58f871aeb26381588d","last_reissued_at":"2026-05-18T01:35:26.332164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:26.332164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02727","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":"2026-05-18T01:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2V06I7A7fPZGAp12YXezgiLn9NvC7zZ6q+sZLt1aCorhOI7p9ylIRcAWwxoJOg2cstkqDsqad0ZUvSHMtv0yAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:13:33.536554Z"},"content_sha256":"5202c165beedba02710d02264cb1340373e904ba47ed014adb324ebe0922bbb3","schema_version":"1.0","event_id":"sha256:5202c165beedba02710d02264cb1340373e904ba47ed014adb324ebe0922bbb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SOVMJWWDMUSFZ7EPLGAEEXM65N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"S^1-equivariant Yamabe invariant of 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bernd Ammann, Farid Madani, Mihaela Pilca","submitted_at":"2015-08-11T20:13:23Z","abstract_excerpt":"We show that the S^1-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the S^1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S^1-action. Furthermore, we prove a convergence result for the equivariant Yamabe constants of an accumulating sequence of subgroups of a compact Lie group acting on a closed manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02727","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":"2026-05-18T01:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMGOaxTxbSUJ85CmZ31lFcMwaZvPIw3i9VlR47A/ur/g0qw37N0a7+LScDZ76ym+YeSsIpRRnhCO5k4EOvU/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:13:33.536894Z"},"content_sha256":"0c5944f767d1acbf94f919a35b6b5c44de1f44694422ebd7f90195e2b13ac3bd","schema_version":"1.0","event_id":"sha256:0c5944f767d1acbf94f919a35b6b5c44de1f44694422ebd7f90195e2b13ac3bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/bundle.json","state_url":"https://pith.science/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/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":"2026-05-28T06:13:33Z","links":{"resolver":"https://pith.science/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N","bundle":"https://pith.science/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/bundle.json","state":"https://pith.science/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SOVMJWWDMUSFZ7EPLGAEEXM65N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SOVMJWWDMUSFZ7EPLGAEEXM65N","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":"faad34e449a869411323dfa2917d976fc9cc76cf0c6fd4c6439514082ee0c408","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-11T20:13:23Z","title_canon_sha256":"3d560ac436d4a76e5f659caad7b1e3ddce1fb7173b4b88e0329882da69a49b95"},"schema_version":"1.0","source":{"id":"1508.02727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02727","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02727v1","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02727","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"SOVMJWWDMUSF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOVMJWWDMUSFZ7EP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOVMJWWD","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:0c5944f767d1acbf94f919a35b6b5c44de1f44694422ebd7f90195e2b13ac3bd","target":"graph","created_at":"2026-05-18T01:35:26Z","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 show that the S^1-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the S^1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S^1-action. Furthermore, we prove a convergence result for the equivariant Yamabe constants of an accumulating sequence of subgroups of a compact Lie group acting on a closed manifold.","authors_text":"Bernd Ammann, Farid Madani, Mihaela Pilca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-11T20:13:23Z","title":"S^1-equivariant Yamabe invariant of 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02727","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":"sha256:5202c165beedba02710d02264cb1340373e904ba47ed014adb324ebe0922bbb3","target":"record","created_at":"2026-05-18T01:35:26Z","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":"faad34e449a869411323dfa2917d976fc9cc76cf0c6fd4c6439514082ee0c408","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-11T20:13:23Z","title_canon_sha256":"3d560ac436d4a76e5f659caad7b1e3ddce1fb7173b4b88e0329882da69a49b95"},"schema_version":"1.0","source":{"id":"1508.02727","kind":"arxiv","version":1}},"canonical_sha256":"93aac4dac365245cfc8f5980425d9eeb714696915b989f58f871aeb26381588d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93aac4dac365245cfc8f5980425d9eeb714696915b989f58f871aeb26381588d","first_computed_at":"2026-05-18T01:35:26.332164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:26.332164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQPnMHJVn3qR2Qh+Ixzo9U0L4JrC8lBbr/Gt7njBPmUj6UEkXWvjcgI9fctT9u0PWbtMpRAtlbAiz4rN0w3IBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:26.332826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5202c165beedba02710d02264cb1340373e904ba47ed014adb324ebe0922bbb3","sha256:0c5944f767d1acbf94f919a35b6b5c44de1f44694422ebd7f90195e2b13ac3bd"],"state_sha256":"ae2d0c25898115dacd7d4992ab13a1c40210907c5065e88fa2bec51cd448b777"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1taK//W7LYy4XeCZt0efDIigc9LrF3kDHqS5x9Ep/wuKL6yFKVL8ADgN5rJrK7BpWislyuc9zz4Bu8rGAToqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:13:33.538839Z","bundle_sha256":"90eae9554c34c8af8d6a5f9a02f37e73263d1cf1802b476f79752d3418c2a94d"}}