{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TXGLWT6OAZOAMTOEHHAYENKV7F","short_pith_number":"pith:TXGLWT6O","canonical_record":{"source":{"id":"1012.4414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T17:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"b1fab2b2e52600724068194e19e349f1a3ac355e9f035085ca427f111543b3c6","abstract_canon_sha256":"2720a711632eea5e789614a01ff2ba20b78337b9937a16cdddf6762f2849bdcd"},"schema_version":"1.0"},"canonical_sha256":"9dccbb4fce065c064dc439c1823555f97c89333e24305fe2fa61266354029b47","source":{"kind":"arxiv","id":"1012.4414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4414","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4414v1","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4414","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"TXGLWT6OAZOA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TXGLWT6OAZOAMTOE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TXGLWT6O","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TXGLWT6OAZOAMTOEHHAYENKV7F","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T17:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"b1fab2b2e52600724068194e19e349f1a3ac355e9f035085ca427f111543b3c6","abstract_canon_sha256":"2720a711632eea5e789614a01ff2ba20b78337b9937a16cdddf6762f2849bdcd"},"schema_version":"1.0"},"canonical_sha256":"9dccbb4fce065c064dc439c1823555f97c89333e24305fe2fa61266354029b47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:54.836153Z","signature_b64":"1m6kcRkxzQbFccik4DusdAnYJtPnqD2yTd1zwbeMuP17l8aTgCGOfTRoIsdCW/BnvS4vmXOGHUmFLiU3ZU4iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dccbb4fce065c064dc439c1823555f97c89333e24305fe2fa61266354029b47","last_reissued_at":"2026-05-18T04:32:54.835558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:54.835558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4414","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MWaICcu1/rua5uMkdhEoXGbcvaAz6OPmyg6MDCec+Yf6lZtp6on79ORtF5vyUqpEW+cXPE7aDMl02p7y649QAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:39.799813Z"},"content_sha256":"43a030332abd6bafa826900553a6ec0693fdf4f959ffd5d620428539c220975f","schema_version":"1.0","event_id":"sha256:43a030332abd6bafa826900553a6ec0693fdf4f959ffd5d620428539c220975f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TXGLWT6OAZOAMTOEHHAYENKV7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Masse des op\\'erateurs GJMS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beno\\^it Michel","submitted_at":"2010-12-20T17:28:35Z","abstract_excerpt":"This work generalizes a construction by Habermann and Jost of a canonical metric in a Yamabe-positive conformal class, which uses the Green function of the conformal Laplacian. In dimension $n=2k+1$, $2k+2$, or $2k+3$, if the $k$-th GJMS operator $P_k$ admits a Green function, the constant term of its singularity is shown to be a conformal density of weight $2k-n$, when restricted to appropriate choices of conformal factor. When it is positive, it is used to build a canonical metric in the conformal class. In the case of the Paneitz-Branson operator $P_2$, in dimension 5, 6 or 7, we show a pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4414","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhdaFzPEwVWD4A5Zo023bIlJ2WEBAklXoE4zLqSxRINfGZ0UfBPBGKuqLCEKl3XLRaOksUafSDllAzxRb87SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:39.800161Z"},"content_sha256":"f4850cdb9a5c5879d230d8200d5445bf8a62e91a27d3726938108a83dcc71f04","schema_version":"1.0","event_id":"sha256:f4850cdb9a5c5879d230d8200d5445bf8a62e91a27d3726938108a83dcc71f04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/bundle.json","state_url":"https://pith.science/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/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":"2026-07-01T21:19:39Z","links":{"resolver":"https://pith.science/pith/TXGLWT6OAZOAMTOEHHAYENKV7F","bundle":"https://pith.science/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/bundle.json","state":"https://pith.science/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXGLWT6OAZOAMTOEHHAYENKV7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TXGLWT6OAZOAMTOEHHAYENKV7F","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":"2720a711632eea5e789614a01ff2ba20b78337b9937a16cdddf6762f2849bdcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T17:28:35Z","title_canon_sha256":"b1fab2b2e52600724068194e19e349f1a3ac355e9f035085ca427f111543b3c6"},"schema_version":"1.0","source":{"id":"1012.4414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4414","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4414v1","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4414","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"TXGLWT6OAZOA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TXGLWT6OAZOAMTOE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TXGLWT6O","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:f4850cdb9a5c5879d230d8200d5445bf8a62e91a27d3726938108a83dcc71f04","target":"graph","created_at":"2026-05-18T04:32:54Z","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":"This work generalizes a construction by Habermann and Jost of a canonical metric in a Yamabe-positive conformal class, which uses the Green function of the conformal Laplacian. In dimension $n=2k+1$, $2k+2$, or $2k+3$, if the $k$-th GJMS operator $P_k$ admits a Green function, the constant term of its singularity is shown to be a conformal density of weight $2k-n$, when restricted to appropriate choices of conformal factor. When it is positive, it is used to build a canonical metric in the conformal class. In the case of the Paneitz-Branson operator $P_2$, in dimension 5, 6 or 7, we show a pos","authors_text":"Beno\\^it Michel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T17:28:35Z","title":"Masse des op\\'erateurs GJMS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4414","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":"sha256:43a030332abd6bafa826900553a6ec0693fdf4f959ffd5d620428539c220975f","target":"record","created_at":"2026-05-18T04:32:54Z","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":"2720a711632eea5e789614a01ff2ba20b78337b9937a16cdddf6762f2849bdcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T17:28:35Z","title_canon_sha256":"b1fab2b2e52600724068194e19e349f1a3ac355e9f035085ca427f111543b3c6"},"schema_version":"1.0","source":{"id":"1012.4414","kind":"arxiv","version":1}},"canonical_sha256":"9dccbb4fce065c064dc439c1823555f97c89333e24305fe2fa61266354029b47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dccbb4fce065c064dc439c1823555f97c89333e24305fe2fa61266354029b47","first_computed_at":"2026-05-18T04:32:54.835558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:54.835558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1m6kcRkxzQbFccik4DusdAnYJtPnqD2yTd1zwbeMuP17l8aTgCGOfTRoIsdCW/BnvS4vmXOGHUmFLiU3ZU4iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:54.836153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43a030332abd6bafa826900553a6ec0693fdf4f959ffd5d620428539c220975f","sha256:f4850cdb9a5c5879d230d8200d5445bf8a62e91a27d3726938108a83dcc71f04"],"state_sha256":"160772dbacbc8fb48dbb63b5b0804bb7e006d718e50bf2b2beb202278a76b97e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pnyP9sGt/ATGpsAsoapw2k6XGQA/E9aEpdTxFkA8YALM5hW4QdGMZ0EIqxhxn3nUAqtjVm8aLDQRTgRok/EoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:19:39.802494Z","bundle_sha256":"0c4b0dfe572513a31b8ecfda49add700b5932fafd6775aab709bd384813d5936"}}