{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7L4ZC4CEEJ4GKMUYJ5SOI6O7G3","short_pith_number":"pith:7L4ZC4CE","canonical_record":{"source":{"id":"1504.05741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T11:33:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"537fae9d7bf6e025aec6c39f90eaa492d9aee722b16d1c929f7976fe9ee80500","abstract_canon_sha256":"730a56cbaf9ed3b48bf5a37c62fe23c025007889ac236a4cdbb4efef0885c9ec"},"schema_version":"1.0"},"canonical_sha256":"faf991704422786532984f64e479df36c1441e2a3e67bdf2826570ba20cd037a","source":{"kind":"arxiv","id":"1504.05741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05741","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05741v1","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05741","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"7L4ZC4CEEJ4G","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L4ZC4CEEJ4GKMUY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L4ZC4CE","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7L4ZC4CEEJ4GKMUYJ5SOI6O7G3","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T11:33:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"537fae9d7bf6e025aec6c39f90eaa492d9aee722b16d1c929f7976fe9ee80500","abstract_canon_sha256":"730a56cbaf9ed3b48bf5a37c62fe23c025007889ac236a4cdbb4efef0885c9ec"},"schema_version":"1.0"},"canonical_sha256":"faf991704422786532984f64e479df36c1441e2a3e67bdf2826570ba20cd037a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:12.798914Z","signature_b64":"6Jx2fmxLPS+c0qJBvHKL4rWPZZXedKDpgyA0rTehzHYESHPl1E/4jiXVLCqkEU1Im0hXLHYQgmzw9tx6HJDQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf991704422786532984f64e479df36c1441e2a3e67bdf2826570ba20cd037a","last_reissued_at":"2026-05-18T02:18:12.798395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:12.798395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05741","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":"2026-05-18T02:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IA4e9av0yF0c92gOrgvBJ52qFIH5ZI6GS4+nUgCAJ8dneKPaxx3mPFhsuUY/CbG/rSu/Z3WAGTufE807QVQODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:54:12.358341Z"},"content_sha256":"22b30f63e5093d5af4e817b3b4ea3c4419ad906f0d5e9b84e4a6095ddd35d47f","schema_version":"1.0","event_id":"sha256:22b30f63e5093d5af4e817b3b4ea3c4419ad906f0d5e9b84e4a6095ddd35d47f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7L4ZC4CEEJ4GKMUYJ5SOI6O7G3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of the ends of the moduli space of anti-self-dual connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Paul M. N. Feehan","submitted_at":"2015-04-22T11:33:39Z","abstract_excerpt":"Let $X$ be a closed, four-dimensional, oriented, smooth manifold with a Riemannian metric, $g$, let $G$ be a compact Lie group, and $P$ be a principal $G$ bundle over $X$. D. Groisser and T. Parker (1987, 1989) and S. K. Donaldson (1990) conjectured that the moduli space of $g$-anti-self-dual connections on $P$, endowed with the $L^2$ metric, has finite volume and diameter. The purpose of this article is to prove this conjecture under the following additional hypotheses. Suppose that $g$ is generic and $X$ is simply-connected. If (i) $G=SU(2)$ or $SO(3)$ and $b^+(X)=0$ or (ii) $G=SO(3)$ and $w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05741","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":"2026-05-18T02:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UMDPvCQvp6PKTQQI5YRFb00FwH96mDl8Jrp7UsnKfjiGgDcEt4CuV8LX8jIdEL0XlqgRAvicJnoFbrbiXn0GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:54:12.358719Z"},"content_sha256":"fa99fadf851f42c2416e5bc29fbb3f13b549acf77e90a1df59a992118c082c89","schema_version":"1.0","event_id":"sha256:fa99fadf851f42c2416e5bc29fbb3f13b549acf77e90a1df59a992118c082c89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/bundle.json","state_url":"https://pith.science/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/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":"2026-06-03T07:54:12Z","links":{"resolver":"https://pith.science/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3","bundle":"https://pith.science/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/bundle.json","state":"https://pith.science/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L4ZC4CEEJ4GKMUYJ5SOI6O7G3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7L4ZC4CEEJ4GKMUYJ5SOI6O7G3","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":"730a56cbaf9ed3b48bf5a37c62fe23c025007889ac236a4cdbb4efef0885c9ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T11:33:39Z","title_canon_sha256":"537fae9d7bf6e025aec6c39f90eaa492d9aee722b16d1c929f7976fe9ee80500"},"schema_version":"1.0","source":{"id":"1504.05741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05741","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05741v1","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05741","created_at":"2026-05-18T02:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"7L4ZC4CEEJ4G","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L4ZC4CEEJ4GKMUY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L4ZC4CE","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:fa99fadf851f42c2416e5bc29fbb3f13b549acf77e90a1df59a992118c082c89","target":"graph","created_at":"2026-05-18T02:18:12Z","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 $X$ be a closed, four-dimensional, oriented, smooth manifold with a Riemannian metric, $g$, let $G$ be a compact Lie group, and $P$ be a principal $G$ bundle over $X$. D. Groisser and T. Parker (1987, 1989) and S. K. Donaldson (1990) conjectured that the moduli space of $g$-anti-self-dual connections on $P$, endowed with the $L^2$ metric, has finite volume and diameter. The purpose of this article is to prove this conjecture under the following additional hypotheses. Suppose that $g$ is generic and $X$ is simply-connected. If (i) $G=SU(2)$ or $SO(3)$ and $b^+(X)=0$ or (ii) $G=SO(3)$ and $w","authors_text":"Paul M. N. Feehan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T11:33:39Z","title":"Geometry of the ends of the moduli space of anti-self-dual connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05741","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":"sha256:22b30f63e5093d5af4e817b3b4ea3c4419ad906f0d5e9b84e4a6095ddd35d47f","target":"record","created_at":"2026-05-18T02:18:12Z","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":"730a56cbaf9ed3b48bf5a37c62fe23c025007889ac236a4cdbb4efef0885c9ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T11:33:39Z","title_canon_sha256":"537fae9d7bf6e025aec6c39f90eaa492d9aee722b16d1c929f7976fe9ee80500"},"schema_version":"1.0","source":{"id":"1504.05741","kind":"arxiv","version":1}},"canonical_sha256":"faf991704422786532984f64e479df36c1441e2a3e67bdf2826570ba20cd037a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf991704422786532984f64e479df36c1441e2a3e67bdf2826570ba20cd037a","first_computed_at":"2026-05-18T02:18:12.798395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:12.798395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Jx2fmxLPS+c0qJBvHKL4rWPZZXedKDpgyA0rTehzHYESHPl1E/4jiXVLCqkEU1Im0hXLHYQgmzw9tx6HJDQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:12.798914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22b30f63e5093d5af4e817b3b4ea3c4419ad906f0d5e9b84e4a6095ddd35d47f","sha256:fa99fadf851f42c2416e5bc29fbb3f13b549acf77e90a1df59a992118c082c89"],"state_sha256":"46dba55aca93fa15d09bc694f68bc8c5f4ea35d7bd731525023cd300df99fe63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mj0Z/cC+x11ej4Il5cC4yfmxYpQy2gW2qKOCKWQplPWV4mb873sLkiS3tY9I8z8zrhMu66dRf8+3vfI+5tZWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:54:12.361848Z","bundle_sha256":"60265643a3db2bcc0b994f953fd415b8f2878561635d9c8cd9b220089c12df8c"}}