{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NN4A6R3BOQWRMJGVKN4TCYJWTU","short_pith_number":"pith:NN4A6R3B","canonical_record":{"source":{"id":"2504.14455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-20T02:18:06Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"8e26ca65ce4cd5580978f3e90f2c9cf3834399dd70a81b79162a160b9f6b034a","abstract_canon_sha256":"90498b31a8b543dec206df125291fc22046b9ea41d757aeff8645de9f05bda6d"},"schema_version":"1.0"},"canonical_sha256":"6b780f4761742d1624d553793161369d23da87c5dc9a7782acb641dc5f013e22","source":{"kind":"arxiv","id":"2504.14455","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14455","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14455v3","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14455","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"NN4A6R3BOQWR","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"NN4A6R3BOQWRMJGV","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"NN4A6R3B","created_at":"2026-06-02T03:04:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NN4A6R3BOQWRMJGVKN4TCYJWTU","target":"record","payload":{"canonical_record":{"source":{"id":"2504.14455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-20T02:18:06Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"8e26ca65ce4cd5580978f3e90f2c9cf3834399dd70a81b79162a160b9f6b034a","abstract_canon_sha256":"90498b31a8b543dec206df125291fc22046b9ea41d757aeff8645de9f05bda6d"},"schema_version":"1.0"},"canonical_sha256":"6b780f4761742d1624d553793161369d23da87c5dc9a7782acb641dc5f013e22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:32.257620Z","signature_b64":"sJORJzqkPGO9C575jUA5xpt2BYfmQAm1zsbqSkEfBH1mrMjTHJvTrVF5OyepYui4vtpxSDEOEb1wwQAd0zUDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b780f4761742d1624d553793161369d23da87c5dc9a7782acb641dc5f013e22","last_reissued_at":"2026-06-02T03:04:32.257108Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:32.257108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.14455","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":"2026-06-02T03:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQGfcOXiEPdPbc3rBYvjTp/XoIXHvar/uVaESFLaONJpFDxJsgzWj7NtSb7UH48PMIxvhIBsX4F5Itk+9R3fAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:55.310596Z"},"content_sha256":"9d35f495101354603562d527a2e76b4c6568505b0a5f6db6803f7fd3be9b0016","schema_version":"1.0","event_id":"sha256:9d35f495101354603562d527a2e76b4c6568505b0a5f6db6803f7fd3be9b0016"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NN4A6R3BOQWRMJGVKN4TCYJWTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological regularity of Busemann spaces of nonpositive curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Shijie Gu, Tadashi Fujioka","submitted_at":"2025-04-20T02:18:06Z","abstract_excerpt":"We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We give a characterization of locally BNPC topological manifolds in terms of their links and show that the singular set of a locally BNPC homology manifold is discrete. We also prove that any (globally) BNPC topological 4-manifold is homeomorphic to Euclidean space. Applications include a topological stability theorem for locally BNPC G-spaces. Our arguments also apply to spaces admitting convex geodesic bicombings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14455","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.14455/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-02T03:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EplrGLRvoOsegKoE6i47tfs1ONnz427l8vvHKauTHp4jzjZAIPflQcAkM9aZfdatZXMhrXD1hEZYGmT3nM+DCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:55.311335Z"},"content_sha256":"94d5f44eb7b2a25e1cf8752603fd930c6f40c581ead6a7a7810985e6c518c15c","schema_version":"1.0","event_id":"sha256:94d5f44eb7b2a25e1cf8752603fd930c6f40c581ead6a7a7810985e6c518c15c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/bundle.json","state_url":"https://pith.science/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/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":"2026-06-12T00:13:55Z","links":{"resolver":"https://pith.science/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU","bundle":"https://pith.science/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/bundle.json","state":"https://pith.science/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NN4A6R3BOQWRMJGVKN4TCYJWTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NN4A6R3BOQWRMJGVKN4TCYJWTU","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":"90498b31a8b543dec206df125291fc22046b9ea41d757aeff8645de9f05bda6d","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-20T02:18:06Z","title_canon_sha256":"8e26ca65ce4cd5580978f3e90f2c9cf3834399dd70a81b79162a160b9f6b034a"},"schema_version":"1.0","source":{"id":"2504.14455","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14455","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14455v3","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14455","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"NN4A6R3BOQWR","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"NN4A6R3BOQWRMJGV","created_at":"2026-06-02T03:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"NN4A6R3B","created_at":"2026-06-02T03:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:94d5f44eb7b2a25e1cf8752603fd930c6f40c581ead6a7a7810985e6c518c15c","target":"graph","created_at":"2026-06-02T03:04:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.14455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We give a characterization of locally BNPC topological manifolds in terms of their links and show that the singular set of a locally BNPC homology manifold is discrete. We also prove that any (globally) BNPC topological 4-manifold is homeomorphic to Euclidean space. Applications include a topological stability theorem for locally BNPC G-spaces. Our arguments also apply to spaces admitting convex geodesic bicombings.","authors_text":"Shijie Gu, Tadashi Fujioka","cross_cats":["math.GT","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-20T02:18:06Z","title":"Topological regularity of Busemann spaces of nonpositive curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14455","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":"sha256:9d35f495101354603562d527a2e76b4c6568505b0a5f6db6803f7fd3be9b0016","target":"record","created_at":"2026-06-02T03:04:32Z","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":"90498b31a8b543dec206df125291fc22046b9ea41d757aeff8645de9f05bda6d","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-20T02:18:06Z","title_canon_sha256":"8e26ca65ce4cd5580978f3e90f2c9cf3834399dd70a81b79162a160b9f6b034a"},"schema_version":"1.0","source":{"id":"2504.14455","kind":"arxiv","version":3}},"canonical_sha256":"6b780f4761742d1624d553793161369d23da87c5dc9a7782acb641dc5f013e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b780f4761742d1624d553793161369d23da87c5dc9a7782acb641dc5f013e22","first_computed_at":"2026-06-02T03:04:32.257108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:32.257108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sJORJzqkPGO9C575jUA5xpt2BYfmQAm1zsbqSkEfBH1mrMjTHJvTrVF5OyepYui4vtpxSDEOEb1wwQAd0zUDDg==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:32.257620Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.14455","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d35f495101354603562d527a2e76b4c6568505b0a5f6db6803f7fd3be9b0016","sha256:94d5f44eb7b2a25e1cf8752603fd930c6f40c581ead6a7a7810985e6c518c15c"],"state_sha256":"878d5b2431d4527402aa9343bb97ce321dbc419a43e307d8b7ab831113201a39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ygp1EXLBg8l1XdbjGmRMhu1j+epRcFah3roOvcDr4dkpYOdIqGyDN4gwQ5maatuZr0DF7pcUqv7yljoqyBNmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:13:55.315238Z","bundle_sha256":"6706373e061527b02c95b0d9671f178bb74d3cd5dea9ea3e1fa9795d1d0073d9"}}