{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U4LIX2Q5TPBNBUWOEHNBSLM4CK","short_pith_number":"pith:U4LIX2Q5","canonical_record":{"source":{"id":"1311.2170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-09T14:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"0ec7fbd206e5174c1c1776bdaa9bbffdce09d10f91014b156798a6f6029c6ca1","abstract_canon_sha256":"c3c69bab45f6d35f89c4f611bcd08b2260d971f18c70cdcb3a54dc93f9d4e4f1"},"schema_version":"1.0"},"canonical_sha256":"a7168bea1d9bc2d0d2ce21da192d9c12b8a1d6504dbd875c728caba6b0f1b82b","source":{"kind":"arxiv","id":"1311.2170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2170","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2170v1","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2170","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"U4LIX2Q5TPBN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4LIX2Q5TPBNBUWO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4LIX2Q5","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U4LIX2Q5TPBNBUWOEHNBSLM4CK","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-09T14:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"0ec7fbd206e5174c1c1776bdaa9bbffdce09d10f91014b156798a6f6029c6ca1","abstract_canon_sha256":"c3c69bab45f6d35f89c4f611bcd08b2260d971f18c70cdcb3a54dc93f9d4e4f1"},"schema_version":"1.0"},"canonical_sha256":"a7168bea1d9bc2d0d2ce21da192d9c12b8a1d6504dbd875c728caba6b0f1b82b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:39.453901Z","signature_b64":"ZJmuyS2xDPBP/Fzd6MeSTjPmxxDIjYAJjznTGedBpSb3iviN3JWnv2Qznkem/qoe6YO2O9fmz0qJwikDjoFSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7168bea1d9bc2d0d2ce21da192d9c12b8a1d6504dbd875c728caba6b0f1b82b","last_reissued_at":"2026-05-18T02:16:39.453453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:39.453453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2170","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":"2026-05-18T02:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hG5iVQ3LA+MnVq60ceKLDKpw84p2D1uO1VGMhYr/4l8LazZeQcGB3FzYJJRQndkzGlLZC3fN1ZagRwpzqrgCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:16:24.012182Z"},"content_sha256":"ad8d76aeb5d6b4891a827a9e7f406fa56c8405917302a27b56876dcf4fb68a3e","schema_version":"1.0","event_id":"sha256:ad8d76aeb5d6b4891a827a9e7f406fa56c8405917302a27b56876dcf4fb68a3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U4LIX2Q5TPBNBUWOEHNBSLM4CK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits, the thesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maja Resman","submitted_at":"2013-11-09T14:00:25Z","abstract_excerpt":"The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and their appropriate generalizations, or, in wider sense, to the epsilon-neighborhoods of sets, for small, positive values of parameter epsilon. In the first part of the thesis, we consider the relation between the multiplicity of the fixed point of a real-line diffeomorphism, and the asymptotic behavior of the length of the epsilon-neighborhoods of its orbits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2170","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":"2026-05-18T02:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9HLTzNxy1xlLto5Imu+nwmoALi4f+EnzcwJaVass0+1Kg/lBEBVEYQ/rp23W7xSVmjiED3NKMHDWG45HCXRmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:16:24.012543Z"},"content_sha256":"34fb4e2a6679dbf642fc6c35e8f45b7f09428b7bd96b8bf02458d8a20fa60246","schema_version":"1.0","event_id":"sha256:34fb4e2a6679dbf642fc6c35e8f45b7f09428b7bd96b8bf02458d8a20fa60246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/bundle.json","state_url":"https://pith.science/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/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":"2026-06-27T12:16:24Z","links":{"resolver":"https://pith.science/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK","bundle":"https://pith.science/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/bundle.json","state":"https://pith.science/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4LIX2Q5TPBNBUWOEHNBSLM4CK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U4LIX2Q5TPBNBUWOEHNBSLM4CK","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":"c3c69bab45f6d35f89c4f611bcd08b2260d971f18c70cdcb3a54dc93f9d4e4f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-09T14:00:25Z","title_canon_sha256":"0ec7fbd206e5174c1c1776bdaa9bbffdce09d10f91014b156798a6f6029c6ca1"},"schema_version":"1.0","source":{"id":"1311.2170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2170","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2170v1","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2170","created_at":"2026-05-18T02:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"U4LIX2Q5TPBN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4LIX2Q5TPBNBUWO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4LIX2Q5","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:34fb4e2a6679dbf642fc6c35e8f45b7f09428b7bd96b8bf02458d8a20fa60246","target":"graph","created_at":"2026-05-18T02:16:39Z","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":"The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and their appropriate generalizations, or, in wider sense, to the epsilon-neighborhoods of sets, for small, positive values of parameter epsilon. In the first part of the thesis, we consider the relation between the multiplicity of the fixed point of a real-line diffeomorphism, and the asymptotic behavior of the length of the epsilon-neighborhoods of its orbits.","authors_text":"Maja Resman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-09T14:00:25Z","title":"Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits, the thesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2170","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:ad8d76aeb5d6b4891a827a9e7f406fa56c8405917302a27b56876dcf4fb68a3e","target":"record","created_at":"2026-05-18T02:16:39Z","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":"c3c69bab45f6d35f89c4f611bcd08b2260d971f18c70cdcb3a54dc93f9d4e4f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-09T14:00:25Z","title_canon_sha256":"0ec7fbd206e5174c1c1776bdaa9bbffdce09d10f91014b156798a6f6029c6ca1"},"schema_version":"1.0","source":{"id":"1311.2170","kind":"arxiv","version":1}},"canonical_sha256":"a7168bea1d9bc2d0d2ce21da192d9c12b8a1d6504dbd875c728caba6b0f1b82b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7168bea1d9bc2d0d2ce21da192d9c12b8a1d6504dbd875c728caba6b0f1b82b","first_computed_at":"2026-05-18T02:16:39.453453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:39.453453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJmuyS2xDPBP/Fzd6MeSTjPmxxDIjYAJjznTGedBpSb3iviN3JWnv2Qznkem/qoe6YO2O9fmz0qJwikDjoFSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:39.453901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad8d76aeb5d6b4891a827a9e7f406fa56c8405917302a27b56876dcf4fb68a3e","sha256:34fb4e2a6679dbf642fc6c35e8f45b7f09428b7bd96b8bf02458d8a20fa60246"],"state_sha256":"9ab0ca2c49ae1f5efc2099d8d8b19a1ac6eb2d0cac7306f7c43156e10de5f092"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7PVbsoQARqR8mistwUGO/EstulFQ5k8rW9+FzlAUzyQlDJX5Lkh+N30fPIlRUHOOqIUrDzR5FiFeoAOAXSwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:16:24.014433Z","bundle_sha256":"e4699b57f0d2e19fe5af21e7ac7a4062ea9ea146821583dea73ba96494fb25eb"}}