{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TP3XBZXZG6Q6FY2HB46SCWFRLS","short_pith_number":"pith:TP3XBZXZ","canonical_record":{"source":{"id":"1606.08082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-26T20:25:35Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7f632429c2edfeeb54ff85f9f332a00331945322d0d36647ae8cab42f3a56c4e","abstract_canon_sha256":"c8f7b891bf3debe8bfb1963fa2bad921320c7dbe6daae7a5fcb57d022b7987e3"},"schema_version":"1.0"},"canonical_sha256":"9bf770e6f937a1e2e3470f3d2158b15c8d49f0a1a72b7de7ea1e572074325eda","source":{"kind":"arxiv","id":"1606.08082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08082","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08082v1","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08082","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"TP3XBZXZG6Q6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TP3XBZXZG6Q6FY2H","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TP3XBZXZ","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TP3XBZXZG6Q6FY2HB46SCWFRLS","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-26T20:25:35Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7f632429c2edfeeb54ff85f9f332a00331945322d0d36647ae8cab42f3a56c4e","abstract_canon_sha256":"c8f7b891bf3debe8bfb1963fa2bad921320c7dbe6daae7a5fcb57d022b7987e3"},"schema_version":"1.0"},"canonical_sha256":"9bf770e6f937a1e2e3470f3d2158b15c8d49f0a1a72b7de7ea1e572074325eda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.801743Z","signature_b64":"QPu5uUJB8COmz6gHeZJT0jOOK9JMLsZo9RJEeLdPLMXNsc1FrrepabLe5aaWGjE1uUZVlS/ISha3KcxQ3hLNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bf770e6f937a1e2e3470f3d2158b15c8d49f0a1a72b7de7ea1e572074325eda","last_reissued_at":"2026-05-18T01:11:52.801394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.801394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08082","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":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppZVjOtsck3wgeLn/fBWwwOGPYu22Lyd4SVuZaWAFK91Sb1AqMBXINxNEfL1mrmCyU75VeBMn+rP2mN7xxbtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:27:16.378655Z"},"content_sha256":"dcb782fc51fdc0e73507c67190c49c8466b6bf84f6e011f53d1b5604e0ce5f05","schema_version":"1.0","event_id":"sha256:dcb782fc51fdc0e73507c67190c49c8466b6bf84f6e011f53d1b5604e0ce5f05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TP3XBZXZG6Q6FY2HB46SCWFRLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Besov spaces via hyperbolic fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Tom\\'as Soto","submitted_at":"2016-06-26T20:25:35Z","abstract_excerpt":"We establish a new characterization of the homogeneous Besov spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ with smoothness $s \\in (0,1)$ in the setting of doubling metric measure spaces $(Z,d,\\mu)$. The characterization is given in terms of a hyperbolic filling of the metric space $(Z,d)$, a construction which has previously appeared in the context of other function spaces in [3,1,2]. We use the characterization to obtain results concerning the density of Lipschitz functions in the spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ and a general complex interpolation formula in the smoothness range $0 < s < 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08082","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":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYEjRJtR6K2ecxCjgsHOtYudWnPmVfuxsLt9PhXi3U8u+0x5OjF8SvfvqDY6VUg4V7jaAnpHlqg0EiNTN0mpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:27:16.379249Z"},"content_sha256":"8d4dc7e551b26514aaf597d9929d4e55cd576636d5a491de79dc1ae1a5e4415b","schema_version":"1.0","event_id":"sha256:8d4dc7e551b26514aaf597d9929d4e55cd576636d5a491de79dc1ae1a5e4415b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/bundle.json","state_url":"https://pith.science/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/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":"2026-07-01T08:27:16Z","links":{"resolver":"https://pith.science/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS","bundle":"https://pith.science/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/bundle.json","state":"https://pith.science/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TP3XBZXZG6Q6FY2HB46SCWFRLS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TP3XBZXZG6Q6FY2HB46SCWFRLS","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":"c8f7b891bf3debe8bfb1963fa2bad921320c7dbe6daae7a5fcb57d022b7987e3","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-26T20:25:35Z","title_canon_sha256":"7f632429c2edfeeb54ff85f9f332a00331945322d0d36647ae8cab42f3a56c4e"},"schema_version":"1.0","source":{"id":"1606.08082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08082","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08082v1","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08082","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"TP3XBZXZG6Q6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TP3XBZXZG6Q6FY2H","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TP3XBZXZ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:8d4dc7e551b26514aaf597d9929d4e55cd576636d5a491de79dc1ae1a5e4415b","target":"graph","created_at":"2026-05-18T01:11:52Z","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 establish a new characterization of the homogeneous Besov spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ with smoothness $s \\in (0,1)$ in the setting of doubling metric measure spaces $(Z,d,\\mu)$. The characterization is given in terms of a hyperbolic filling of the metric space $(Z,d)$, a construction which has previously appeared in the context of other function spaces in [3,1,2]. We use the characterization to obtain results concerning the density of Lipschitz functions in the spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ and a general complex interpolation formula in the smoothness range $0 < s < 1$.","authors_text":"Tom\\'as Soto","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-26T20:25:35Z","title":"Besov spaces via hyperbolic fillings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08082","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:dcb782fc51fdc0e73507c67190c49c8466b6bf84f6e011f53d1b5604e0ce5f05","target":"record","created_at":"2026-05-18T01:11:52Z","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":"c8f7b891bf3debe8bfb1963fa2bad921320c7dbe6daae7a5fcb57d022b7987e3","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-26T20:25:35Z","title_canon_sha256":"7f632429c2edfeeb54ff85f9f332a00331945322d0d36647ae8cab42f3a56c4e"},"schema_version":"1.0","source":{"id":"1606.08082","kind":"arxiv","version":1}},"canonical_sha256":"9bf770e6f937a1e2e3470f3d2158b15c8d49f0a1a72b7de7ea1e572074325eda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bf770e6f937a1e2e3470f3d2158b15c8d49f0a1a72b7de7ea1e572074325eda","first_computed_at":"2026-05-18T01:11:52.801394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:52.801394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QPu5uUJB8COmz6gHeZJT0jOOK9JMLsZo9RJEeLdPLMXNsc1FrrepabLe5aaWGjE1uUZVlS/ISha3KcxQ3hLNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:52.801743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcb782fc51fdc0e73507c67190c49c8466b6bf84f6e011f53d1b5604e0ce5f05","sha256:8d4dc7e551b26514aaf597d9929d4e55cd576636d5a491de79dc1ae1a5e4415b"],"state_sha256":"55ee02f9ead77e416c175dbed4535a72986575720f22eb69c03d21c6836177bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqGIePEbJYc1ChbJb8O38mhTRg3Tm77vwyNlzsQ57V526Fz90oSZnZlnN0UcDLzfqgERrOlpLtHNn72V6VmTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:27:16.382890Z","bundle_sha256":"e2004c8b3fc59bf463c2bd5e8c07968486295c5e413803714cb8f011418046ad"}}