{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MNN5VDJGZWUBWMABBVS3BOY4LQ","short_pith_number":"pith:MNN5VDJG","canonical_record":{"source":{"id":"2605.17130","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-16T19:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"dbc2b998ced9129d21c4d56af3487948586687dce0787f57cfa5b972ffb31879","abstract_canon_sha256":"f2f679a17b8791b1aeeebd048852d11c6407127958eff25261451f120de4dedc"},"schema_version":"1.0"},"canonical_sha256":"635bda8d26cda81b30010d65b0bb1c5c20692238a1f3671bac5e8b1549098c11","source":{"kind":"arxiv","id":"2605.17130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17130","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17130v1","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17130","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"MNN5VDJGZWUB","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_16","alias_value":"MNN5VDJGZWUBWMAB","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_8","alias_value":"MNN5VDJG","created_at":"2026-05-20T00:03:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MNN5VDJGZWUBWMABBVS3BOY4LQ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17130","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-16T19:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"dbc2b998ced9129d21c4d56af3487948586687dce0787f57cfa5b972ffb31879","abstract_canon_sha256":"f2f679a17b8791b1aeeebd048852d11c6407127958eff25261451f120de4dedc"},"schema_version":"1.0"},"canonical_sha256":"635bda8d26cda81b30010d65b0bb1c5c20692238a1f3671bac5e8b1549098c11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:41.425891Z","signature_b64":"b1fc0s6BaVsgIZPO0KiiSkHyCd4byt+NLZB3dG5ghq0VQARj1jhRTpkNmE59Hte1Ccf0dOmvEpgTKWvBl90iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"635bda8d26cda81b30010d65b0bb1c5c20692238a1f3671bac5e8b1549098c11","last_reissued_at":"2026-05-20T00:03:41.425078Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:41.425078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17130","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":"2026-05-20T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SBkeegz3gnCHNLgEj0j23tU2j9QOCq3VLEFA1N1jwOWWuSqDd6pYY/HWlgSHwuHDXpyA+veEypsRGQ6iESVdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:07:03.388425Z"},"content_sha256":"2d14a7e382427143c2b2b8b63cd852939c16934bd09874d9229c9101b9c1d450","schema_version":"1.0","event_id":"sha256:2d14a7e382427143c2b2b8b63cd852939c16934bd09874d9229c9101b9c1d450"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MNN5VDJGZWUBWMABBVS3BOY4LQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On components of stable connectivity of gradient-like diffeomorphisms of the 2-torus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"D.A. Baranov, E.V. Nozdrinova, O.V. Pochinka","submitted_at":"2026-05-16T19:32:40Z","abstract_excerpt":"Gradient-like diffeomorphisms of a closed surface $M^2$ are characterized by a finite hyperbolic limit set and the absence of intersections of invariant manifolds of distinct saddle points. In the case where such diffeomorphisms $f_0, f_1:M^2\\to M^2$ are isotopic, they are connected by some arc $\\{f_t:M^2\\to M^2, t\\in [0,1]\\}$ in the space of diffeomorphisms. If every diffeomorphism of the arc has a finite limit set and the arc is stable (does not change its qualitative properties under small perturbations) in the space of diffeomorphisms, then $f_0,f_1$ are said to be {\\it stably connected}. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17130","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17130/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.778220Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:58.023141Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"65be9c17b981bf25eb61fe85cec81c9dc7635c8eb84f3bb48b4dd5ed7ba69ca0"},"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":"2026-05-20T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0o/81GqqC9H6rA1CC65WLQHzkfOguSZelhSq5dwITrgteYGLOrBhCpYG990tJlU0FzzbbKDfJgS2c0Y3sJw5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:07:03.388840Z"},"content_sha256":"e58f35697fcb04958929b97316877764f2a0ae69670f26c615b3af7adc55035e","schema_version":"1.0","event_id":"sha256:e58f35697fcb04958929b97316877764f2a0ae69670f26c615b3af7adc55035e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/bundle.json","state_url":"https://pith.science/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/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":"2026-06-10T20:07:03Z","links":{"resolver":"https://pith.science/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ","bundle":"https://pith.science/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/bundle.json","state":"https://pith.science/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNN5VDJGZWUBWMABBVS3BOY4LQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MNN5VDJGZWUBWMABBVS3BOY4LQ","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":"f2f679a17b8791b1aeeebd048852d11c6407127958eff25261451f120de4dedc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-16T19:32:40Z","title_canon_sha256":"dbc2b998ced9129d21c4d56af3487948586687dce0787f57cfa5b972ffb31879"},"schema_version":"1.0","source":{"id":"2605.17130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17130","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17130v1","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17130","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"MNN5VDJGZWUB","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_16","alias_value":"MNN5VDJGZWUBWMAB","created_at":"2026-05-20T00:03:41Z"},{"alias_kind":"pith_short_8","alias_value":"MNN5VDJG","created_at":"2026-05-20T00:03:41Z"}],"graph_snapshots":[{"event_id":"sha256:e58f35697fcb04958929b97316877764f2a0ae69670f26c615b3af7adc55035e","target":"graph","created_at":"2026-05-20T00:03:41Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.778220Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T22:01:58.023141Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17130/integrity.json","findings":[],"snapshot_sha256":"65be9c17b981bf25eb61fe85cec81c9dc7635c8eb84f3bb48b4dd5ed7ba69ca0","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-like diffeomorphisms of a closed surface $M^2$ are characterized by a finite hyperbolic limit set and the absence of intersections of invariant manifolds of distinct saddle points. In the case where such diffeomorphisms $f_0, f_1:M^2\\to M^2$ are isotopic, they are connected by some arc $\\{f_t:M^2\\to M^2, t\\in [0,1]\\}$ in the space of diffeomorphisms. If every diffeomorphism of the arc has a finite limit set and the arc is stable (does not change its qualitative properties under small perturbations) in the space of diffeomorphisms, then $f_0,f_1$ are said to be {\\it stably connected}. ","authors_text":"D.A. Baranov, E.V. Nozdrinova, O.V. Pochinka","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-16T19:32:40Z","title":"On components of stable connectivity of gradient-like diffeomorphisms of the 2-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17130","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":"sha256:2d14a7e382427143c2b2b8b63cd852939c16934bd09874d9229c9101b9c1d450","target":"record","created_at":"2026-05-20T00:03:41Z","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":"f2f679a17b8791b1aeeebd048852d11c6407127958eff25261451f120de4dedc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-16T19:32:40Z","title_canon_sha256":"dbc2b998ced9129d21c4d56af3487948586687dce0787f57cfa5b972ffb31879"},"schema_version":"1.0","source":{"id":"2605.17130","kind":"arxiv","version":1}},"canonical_sha256":"635bda8d26cda81b30010d65b0bb1c5c20692238a1f3671bac5e8b1549098c11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"635bda8d26cda81b30010d65b0bb1c5c20692238a1f3671bac5e8b1549098c11","first_computed_at":"2026-05-20T00:03:41.425078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:41.425078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b1fc0s6BaVsgIZPO0KiiSkHyCd4byt+NLZB3dG5ghq0VQARj1jhRTpkNmE59Hte1Ccf0dOmvEpgTKWvBl90iCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:41.425891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d14a7e382427143c2b2b8b63cd852939c16934bd09874d9229c9101b9c1d450","sha256:e58f35697fcb04958929b97316877764f2a0ae69670f26c615b3af7adc55035e"],"state_sha256":"4a89a1ad4ff0b099a9b66c21d93bf43e32f65d5cf2184ebe6f1f66f876f66f82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnPLAVW4EpHADhqYiRlT+oq9YfgJhVnjUfW5dumMalHiOg0yN3HYaz5dEoQA+hHxDsau/G7aoI10H/7wSk7BBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:07:03.390988Z","bundle_sha256":"566489517a0fef6ce144eea5171c9e104dbc3e830fb351aada9de02fc8a011d4"}}