{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NB74NISMO6PUDYEUKC5Q74VAH3","short_pith_number":"pith:NB74NISM","canonical_record":{"source":{"id":"1105.4677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T04:26:14Z","cross_cats_sorted":[],"title_canon_sha256":"1e399605a3b014318dc351e679d71b15cdfa8e6391b9232fd8ba86a77f783aec","abstract_canon_sha256":"dc2579d1cc88c3791e6679a7eb3f313a91654ea7d2093cb2b0bd4ab68c2a398b"},"schema_version":"1.0"},"canonical_sha256":"687fc6a24c779f41e09450bb0ff2a03efb0695942cc6f6712556a59b306c9720","source":{"kind":"arxiv","id":"1105.4677","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4677","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4677v2","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4677","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"NB74NISMO6PU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NB74NISMO6PUDYEU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NB74NISM","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NB74NISMO6PUDYEUKC5Q74VAH3","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T04:26:14Z","cross_cats_sorted":[],"title_canon_sha256":"1e399605a3b014318dc351e679d71b15cdfa8e6391b9232fd8ba86a77f783aec","abstract_canon_sha256":"dc2579d1cc88c3791e6679a7eb3f313a91654ea7d2093cb2b0bd4ab68c2a398b"},"schema_version":"1.0"},"canonical_sha256":"687fc6a24c779f41e09450bb0ff2a03efb0695942cc6f6712556a59b306c9720","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:15.439615Z","signature_b64":"h09lcDHJcfiS5bcSxOieVIlEmDL8/3hsghNaraKS3z1vW2zgHOIGV8F9Ll4xDbsYnRaBUgy5pDYosO6j066VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"687fc6a24c779f41e09450bb0ff2a03efb0695942cc6f6712556a59b306c9720","last_reissued_at":"2026-05-18T02:42:15.438868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:15.438868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4677","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlPJzqLLfn8/ZyGThTHHh3Klg2s66Lqf3QyDw7ulDd/n8nQePhjokuOb94Qv22K8XM5vqyz8RtTlafWaHt/gDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:56:06.707263Z"},"content_sha256":"249dec6abf0d208de9df7162c08f7b9205ab9690543a6e11beea42902dcaf1c3","schema_version":"1.0","event_id":"sha256:249dec6abf0d208de9df7162c08f7b9205ab9690543a6e11beea42902dcaf1c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NB74NISMO6PUDYEUKC5Q74VAH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slow entropy and differentiable models for infinite-measure preserving Z^k actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michael Hochman","submitted_at":"2011-05-24T04:26:14Z","abstract_excerpt":"We define \"slow\" entropy invariants for Z^2 actions on infinite measure spaces, which measures growth of itineraries at subexponential scales. We use this to construct infinite-measure preserving Z^2 actions which cannot be realized as a group of diffeomorphisms of a compact manifold preserving a Borel measure, contrary to the situation for Z-actions, where every infinite-measure preserving action can be realized in this way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4677","kind":"arxiv","version":2},"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":"2026-05-18T02:42:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwsUeTMMStYVmJfGbd1/bt05JlesYAHsXM92qZEBI1pWOl55xT5BI/xFv8mpsgIk7qGUuBBhVQkK9LjiMASxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:56:06.707910Z"},"content_sha256":"694f0b55962f1ad6ad5dfad201e823674c3295c3a13c6254b47155c5db3286c6","schema_version":"1.0","event_id":"sha256:694f0b55962f1ad6ad5dfad201e823674c3295c3a13c6254b47155c5db3286c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NB74NISMO6PUDYEUKC5Q74VAH3/bundle.json","state_url":"https://pith.science/pith/NB74NISMO6PUDYEUKC5Q74VAH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NB74NISMO6PUDYEUKC5Q74VAH3/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":"2026-06-23T07:56:06Z","links":{"resolver":"https://pith.science/pith/NB74NISMO6PUDYEUKC5Q74VAH3","bundle":"https://pith.science/pith/NB74NISMO6PUDYEUKC5Q74VAH3/bundle.json","state":"https://pith.science/pith/NB74NISMO6PUDYEUKC5Q74VAH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NB74NISMO6PUDYEUKC5Q74VAH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NB74NISMO6PUDYEUKC5Q74VAH3","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":"dc2579d1cc88c3791e6679a7eb3f313a91654ea7d2093cb2b0bd4ab68c2a398b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T04:26:14Z","title_canon_sha256":"1e399605a3b014318dc351e679d71b15cdfa8e6391b9232fd8ba86a77f783aec"},"schema_version":"1.0","source":{"id":"1105.4677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4677","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4677v2","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4677","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"NB74NISMO6PU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NB74NISMO6PUDYEU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NB74NISM","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:694f0b55962f1ad6ad5dfad201e823674c3295c3a13c6254b47155c5db3286c6","target":"graph","created_at":"2026-05-18T02:42:15Z","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 define \"slow\" entropy invariants for Z^2 actions on infinite measure spaces, which measures growth of itineraries at subexponential scales. We use this to construct infinite-measure preserving Z^2 actions which cannot be realized as a group of diffeomorphisms of a compact manifold preserving a Borel measure, contrary to the situation for Z-actions, where every infinite-measure preserving action can be realized in this way.","authors_text":"Michael Hochman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T04:26:14Z","title":"Slow entropy and differentiable models for infinite-measure preserving Z^k actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4677","kind":"arxiv","version":2},"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":"sha256:249dec6abf0d208de9df7162c08f7b9205ab9690543a6e11beea42902dcaf1c3","target":"record","created_at":"2026-05-18T02:42:15Z","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":"dc2579d1cc88c3791e6679a7eb3f313a91654ea7d2093cb2b0bd4ab68c2a398b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T04:26:14Z","title_canon_sha256":"1e399605a3b014318dc351e679d71b15cdfa8e6391b9232fd8ba86a77f783aec"},"schema_version":"1.0","source":{"id":"1105.4677","kind":"arxiv","version":2}},"canonical_sha256":"687fc6a24c779f41e09450bb0ff2a03efb0695942cc6f6712556a59b306c9720","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"687fc6a24c779f41e09450bb0ff2a03efb0695942cc6f6712556a59b306c9720","first_computed_at":"2026-05-18T02:42:15.438868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:15.438868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h09lcDHJcfiS5bcSxOieVIlEmDL8/3hsghNaraKS3z1vW2zgHOIGV8F9Ll4xDbsYnRaBUgy5pDYosO6j066VDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:15.439615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:249dec6abf0d208de9df7162c08f7b9205ab9690543a6e11beea42902dcaf1c3","sha256:694f0b55962f1ad6ad5dfad201e823674c3295c3a13c6254b47155c5db3286c6"],"state_sha256":"4e239f0a6e240e52d747788832a248d4e4973bfd811786cfe67555321e26ea4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MCRYGIoMzBgHtM4DtNMHFnioNOuZBtmwx46pVe3F30Pm4lNFd0HuYTj5Ued44NSR0HljNF/Bp6H0pc4NOEdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:56:06.710826Z","bundle_sha256":"7b80b33880aa407cc1ca032c2754e222e824581b46f702b0f84f456f1e51bb1f"}}