{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JPBGZHWP5FM46G565TYVEAOBP2","short_pith_number":"pith:JPBGZHWP","canonical_record":{"source":{"id":"1912.00590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-12-02T06:34:05Z","cross_cats_sorted":["math.AT","math.DG","math.MG"],"title_canon_sha256":"56234b5eb547351b1e6057da70fb984734e6532988c689d8f3e8198c61e7d00a","abstract_canon_sha256":"5b31dbb513d4431a261313d0897b8b2f41e98cb9351aad95bde5c090fcbc10ae"},"schema_version":"1.0"},"canonical_sha256":"4bc26c9ecfe959cf1bbeecf15201c17e880b4b72e86771c7800df5f657ac13bc","source":{"kind":"arxiv","id":"1912.00590","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00590","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00590v3","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00590","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"JPBGZHWP5FM4","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_16","alias_value":"JPBGZHWP5FM46G56","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_8","alias_value":"JPBGZHWP","created_at":"2026-07-05T04:57:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JPBGZHWP5FM46G565TYVEAOBP2","target":"record","payload":{"canonical_record":{"source":{"id":"1912.00590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-12-02T06:34:05Z","cross_cats_sorted":["math.AT","math.DG","math.MG"],"title_canon_sha256":"56234b5eb547351b1e6057da70fb984734e6532988c689d8f3e8198c61e7d00a","abstract_canon_sha256":"5b31dbb513d4431a261313d0897b8b2f41e98cb9351aad95bde5c090fcbc10ae"},"schema_version":"1.0"},"canonical_sha256":"4bc26c9ecfe959cf1bbeecf15201c17e880b4b72e86771c7800df5f657ac13bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:57:41.095368Z","signature_b64":"UUBmaR/gPm5+74ishWjWmAdVdMxZqCl0Cgkrh/sxmNg98CZz7DniQcjf61/tINEjwE9bAt4QGNawGv6x0n75DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc26c9ecfe959cf1bbeecf15201c17e880b4b72e86771c7800df5f657ac13bc","last_reissued_at":"2026-07-05T04:57:41.094965Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:57:41.094965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.00590","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":"2026-07-05T04:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bevlb/Bd/a6dJV31kiE83lkGwgHNAICGMMVH9LrlJ1dzLynGL7KpEnZva+fJJ8YZN2nwc/uflWFXK4HrBbQYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:39:09.030927Z"},"content_sha256":"3fd5c43efee1d90e5694e5567ee58f8bb9bd73c390c097f632b8aa9b220be8a5","schema_version":"1.0","event_id":"sha256:3fd5c43efee1d90e5694e5567ee58f8bb9bd73c390c097f632b8aa9b220be8a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JPBGZHWP5FM46G565TYVEAOBP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG","math.MG"],"primary_cat":"math.GT","authors_text":"Aleksandr Berdnikov, Fedor Manin","submitted_at":"2019-12-02T06:34:05Z","abstract_excerpt":"\\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scalable provide counterexamples to Gromov's long-standing conjecture on distortion in higher homot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00590","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/1912.00590/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":"2026-07-05T04:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"acJVq0j76Jtsc3CpLJEQas/QfaiygzuZuTjaz1BRyJ8Up+jy5PkA8IEvRD+IBt4I/X2mhHT9aOO4qzyXVNdgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:39:09.031867Z"},"content_sha256":"4bc62512ed64d1791860e250ba07e3a232e2358fc5223655284f5d79dbf71429","schema_version":"1.0","event_id":"sha256:4bc62512ed64d1791860e250ba07e3a232e2358fc5223655284f5d79dbf71429"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPBGZHWP5FM46G565TYVEAOBP2/bundle.json","state_url":"https://pith.science/pith/JPBGZHWP5FM46G565TYVEAOBP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPBGZHWP5FM46G565TYVEAOBP2/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":"2026-08-16T07:39:09Z","links":{"resolver":"https://pith.science/pith/JPBGZHWP5FM46G565TYVEAOBP2","bundle":"https://pith.science/pith/JPBGZHWP5FM46G565TYVEAOBP2/bundle.json","state":"https://pith.science/pith/JPBGZHWP5FM46G565TYVEAOBP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPBGZHWP5FM46G565TYVEAOBP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JPBGZHWP5FM46G565TYVEAOBP2","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":"5b31dbb513d4431a261313d0897b8b2f41e98cb9351aad95bde5c090fcbc10ae","cross_cats_sorted":["math.AT","math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-12-02T06:34:05Z","title_canon_sha256":"56234b5eb547351b1e6057da70fb984734e6532988c689d8f3e8198c61e7d00a"},"schema_version":"1.0","source":{"id":"1912.00590","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00590","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00590v3","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00590","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"JPBGZHWP5FM4","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_16","alias_value":"JPBGZHWP5FM46G56","created_at":"2026-07-05T04:57:41Z"},{"alias_kind":"pith_short_8","alias_value":"JPBGZHWP","created_at":"2026-07-05T04:57:41Z"}],"graph_snapshots":[{"event_id":"sha256:4bc62512ed64d1791860e250ba07e3a232e2358fc5223655284f5d79dbf71429","target":"graph","created_at":"2026-07-05T04:57:41Z","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/1912.00590/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"\\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scalable provide counterexamples to Gromov's long-standing conjecture on distortion in higher homot","authors_text":"Aleksandr Berdnikov, Fedor Manin","cross_cats":["math.AT","math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-12-02T06:34:05Z","title":"Scalable spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00590","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":"sha256:3fd5c43efee1d90e5694e5567ee58f8bb9bd73c390c097f632b8aa9b220be8a5","target":"record","created_at":"2026-07-05T04:57:41Z","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":"5b31dbb513d4431a261313d0897b8b2f41e98cb9351aad95bde5c090fcbc10ae","cross_cats_sorted":["math.AT","math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-12-02T06:34:05Z","title_canon_sha256":"56234b5eb547351b1e6057da70fb984734e6532988c689d8f3e8198c61e7d00a"},"schema_version":"1.0","source":{"id":"1912.00590","kind":"arxiv","version":3}},"canonical_sha256":"4bc26c9ecfe959cf1bbeecf15201c17e880b4b72e86771c7800df5f657ac13bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bc26c9ecfe959cf1bbeecf15201c17e880b4b72e86771c7800df5f657ac13bc","first_computed_at":"2026-07-05T04:57:41.094965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:57:41.094965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UUBmaR/gPm5+74ishWjWmAdVdMxZqCl0Cgkrh/sxmNg98CZz7DniQcjf61/tINEjwE9bAt4QGNawGv6x0n75DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:57:41.095368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.00590","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fd5c43efee1d90e5694e5567ee58f8bb9bd73c390c097f632b8aa9b220be8a5","sha256:4bc62512ed64d1791860e250ba07e3a232e2358fc5223655284f5d79dbf71429"],"state_sha256":"895db555c864098b9676259b01aba70008434cfe6c81ee6de0e24778c4fd5bf9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+XI32aEywkU3cZPnUsVtkVSTpPbsp2rsZ+qCE4PnZZyhNsA6V0VVV6CzRn/f8rTLjONAoURWbmDKKLCaNFfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:39:09.039158Z","bundle_sha256":"1a3b95c0461cf1f5856e28e14e8b24d4f43dbb432cc97177e20d582a3f7f9f7c"}}