{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:42BQRQMUYFW4OMHVJUDRCEV3QC","short_pith_number":"pith:42BQRQMU","canonical_record":{"source":{"id":"1211.2872","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-13T02:00:06Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3420ae2fb014ff58653aeb2c345f23c1b6ccafa8e41c16295e9fd30058c4ab69","abstract_canon_sha256":"8e18aeb447af9c424829dc2971ed5cd8f26ae0c27a41c9598f8300be8d84455d"},"schema_version":"1.0"},"canonical_sha256":"e68308c194c16dc730f54d071112bb809b5cee794194bca7ec3f86a6b99315e9","source":{"kind":"arxiv","id":"1211.2872","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2872","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2872v3","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2872","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"42BQRQMUYFW4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"42BQRQMUYFW4OMHV","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"42BQRQMU","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:42BQRQMUYFW4OMHVJUDRCEV3QC","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2872","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-13T02:00:06Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3420ae2fb014ff58653aeb2c345f23c1b6ccafa8e41c16295e9fd30058c4ab69","abstract_canon_sha256":"8e18aeb447af9c424829dc2971ed5cd8f26ae0c27a41c9598f8300be8d84455d"},"schema_version":"1.0"},"canonical_sha256":"e68308c194c16dc730f54d071112bb809b5cee794194bca7ec3f86a6b99315e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.689178Z","signature_b64":"w/7MXjN81yV2+w08qGPblsaPrZm4jn35Y2S2hrTA52o+5rKOaC+osXzFOCBp7QWMQvP6iRLgrVK490qWGXU3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e68308c194c16dc730f54d071112bb809b5cee794194bca7ec3f86a6b99315e9","last_reissued_at":"2026-05-18T02:54:21.688748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.688748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2872","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0q8sJSXQGPKvaVXTT0/yuSbaLzIa6pHgdlreWTtbpPNxYD8wfgqCUfMIgCfrRspyJcW5MlVmF8gadB84sy6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:27:07.853076Z"},"content_sha256":"9287751e8f9c77f6214874a8483b9d3bc0dcda4d6e24dc754b74ae7e5acf12a7","schema_version":"1.0","event_id":"sha256:9287751e8f9c77f6214874a8483b9d3bc0dcda4d6e24dc754b74ae7e5acf12a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:42BQRQMUYFW4OMHVJUDRCEV3QC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inductive topological Hausdorff dimensions and fibers of generic continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CA","authors_text":"Rich\\'ard Balka","submitted_at":"2012-11-13T02:00:06Z","abstract_excerpt":"In an earlier paper Buczolich, Elekes and the author introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. They proved that it is precisely the right notion to describe the Hausdorff dimension of the level sets of the generic real-valued continuous function (in the sense of Baire category) defined on a compact metric space $K$.\n  The goal of this paper is to determine the Hausdorff dimension of the fibers of the generic continuous function from $K$ to $\\mathbb{R}^n$. In order to do so, we define the $n$th inductive topological Hausdorff dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2872","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":""},"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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUqWKAYyw7NT/z1rp6bkM0iJ2E53sa+mSshjW5fgS+Ps8XnC7WhHirDDB2eO1T5NbLvWzLA2gXdRoPAiH7Z7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:27:07.853438Z"},"content_sha256":"383ea00462edeaf58015d53e4e34d406d37c415a5bf0486d9a443ff94bf0dd6c","schema_version":"1.0","event_id":"sha256:383ea00462edeaf58015d53e4e34d406d37c415a5bf0486d9a443ff94bf0dd6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/bundle.json","state_url":"https://pith.science/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/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":"2026-06-22T11:27:07Z","links":{"resolver":"https://pith.science/pith/42BQRQMUYFW4OMHVJUDRCEV3QC","bundle":"https://pith.science/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/bundle.json","state":"https://pith.science/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42BQRQMUYFW4OMHVJUDRCEV3QC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:42BQRQMUYFW4OMHVJUDRCEV3QC","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":"8e18aeb447af9c424829dc2971ed5cd8f26ae0c27a41c9598f8300be8d84455d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-13T02:00:06Z","title_canon_sha256":"3420ae2fb014ff58653aeb2c345f23c1b6ccafa8e41c16295e9fd30058c4ab69"},"schema_version":"1.0","source":{"id":"1211.2872","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2872","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2872v3","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2872","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"42BQRQMUYFW4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"42BQRQMUYFW4OMHV","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"42BQRQMU","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:383ea00462edeaf58015d53e4e34d406d37c415a5bf0486d9a443ff94bf0dd6c","target":"graph","created_at":"2026-05-18T02:54:21Z","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":"In an earlier paper Buczolich, Elekes and the author introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. They proved that it is precisely the right notion to describe the Hausdorff dimension of the level sets of the generic real-valued continuous function (in the sense of Baire category) defined on a compact metric space $K$.\n  The goal of this paper is to determine the Hausdorff dimension of the fibers of the generic continuous function from $K$ to $\\mathbb{R}^n$. In order to do so, we define the $n$th inductive topological Hausdorff dimensi","authors_text":"Rich\\'ard Balka","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-13T02:00:06Z","title":"Inductive topological Hausdorff dimensions and fibers of generic continuous functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2872","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":"sha256:9287751e8f9c77f6214874a8483b9d3bc0dcda4d6e24dc754b74ae7e5acf12a7","target":"record","created_at":"2026-05-18T02:54:21Z","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":"8e18aeb447af9c424829dc2971ed5cd8f26ae0c27a41c9598f8300be8d84455d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-13T02:00:06Z","title_canon_sha256":"3420ae2fb014ff58653aeb2c345f23c1b6ccafa8e41c16295e9fd30058c4ab69"},"schema_version":"1.0","source":{"id":"1211.2872","kind":"arxiv","version":3}},"canonical_sha256":"e68308c194c16dc730f54d071112bb809b5cee794194bca7ec3f86a6b99315e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e68308c194c16dc730f54d071112bb809b5cee794194bca7ec3f86a6b99315e9","first_computed_at":"2026-05-18T02:54:21.688748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.688748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w/7MXjN81yV2+w08qGPblsaPrZm4jn35Y2S2hrTA52o+5rKOaC+osXzFOCBp7QWMQvP6iRLgrVK490qWGXU3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.689178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2872","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9287751e8f9c77f6214874a8483b9d3bc0dcda4d6e24dc754b74ae7e5acf12a7","sha256:383ea00462edeaf58015d53e4e34d406d37c415a5bf0486d9a443ff94bf0dd6c"],"state_sha256":"f8afd3081a03a810bd4305b6bc27b90c92da086742cf9920f0c50be920b282d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cs4U02JSrY/wTQwixgqOZwRnhQgs8+VkPCxCL1f23svzquX9gpOnZDHyzeq/x+yzbRxhCFe/5+Wr+qvuuSpjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:27:07.855423Z","bundle_sha256":"3daa68a90d4e71606d0eb23e8a1c99bc3fdb2ad2890f657f6a3948904cbf32d0"}}