{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2N4J35B2KZ4L3KQJLT3ER35PMF","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":"5a08cb9077877abfa33315a9cb90746f2423cd96bf0b2a638be0e523bb699776","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-09T17:22:08Z","title_canon_sha256":"0630011aafe4887a791d472752b7fc47527f76897484a1ff3625895908b25c01"},"schema_version":"1.0","source":{"id":"1809.03009","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03009","created_at":"2026-05-17T23:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03009v3","created_at":"2026-05-17T23:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03009","created_at":"2026-05-17T23:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"2N4J35B2KZ4L","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2N4J35B2KZ4L3KQJ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2N4J35B2","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:fee074ddeb5da238eaaf86c198859c5b625971bdd65b310dbf6abf833b800c89","target":"graph","created_at":"2026-05-17T23:53:42Z","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":"Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping $f\\colon X\\to Y$ between oriented cohomology manifolds $X$ and $Y$ induces a pull-back operator $f^\\ast \\colon M_{k,loc}(Y) \\to M_{k,loc}(X)$ between the spaces of metric $k$-currents of locally finite mass. For proper maps, the pull-back is a right-inverse (up to multiplicity) of the push-forward $f_\\ast \\colon M_{k,loc}(X)\\to M_{k,loc}(Y)$. As an application we obtain a non-smooth version of the cohomological boundedness theorem of Bonk and Heinonen for locally Lipschitz contractible cohomology $n$-manif","authors_text":"Elefterios Soultanis, Pekka Pankka","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-09T17:22:08Z","title":"Pull-back of metric currents and homological boundedness of BLD-elliptic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03009","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:db3897781c6e5c6f98af5eb782de2cba397ee53c0ef5832136cc5a8e05275145","target":"record","created_at":"2026-05-17T23:53:42Z","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":"5a08cb9077877abfa33315a9cb90746f2423cd96bf0b2a638be0e523bb699776","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-09T17:22:08Z","title_canon_sha256":"0630011aafe4887a791d472752b7fc47527f76897484a1ff3625895908b25c01"},"schema_version":"1.0","source":{"id":"1809.03009","kind":"arxiv","version":3}},"canonical_sha256":"d3789df43a5678bdaa095cf648efaf616288e8c19bd9b73ac85509d97c2e71fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3789df43a5678bdaa095cf648efaf616288e8c19bd9b73ac85509d97c2e71fc","first_computed_at":"2026-05-17T23:53:42.067544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:42.067544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U3fG5AgwIOJEPaeeD6jDx0iHz1gp1g8kbHK6JZJ6o3XBy2gd9rLvPiBHp0ucuUTbEKkPiOVkoRC8zlyGMpStDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:42.068103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03009","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db3897781c6e5c6f98af5eb782de2cba397ee53c0ef5832136cc5a8e05275145","sha256:fee074ddeb5da238eaaf86c198859c5b625971bdd65b310dbf6abf833b800c89"],"state_sha256":"4223f9caa7748a1c7cd3e8082c6bf4b13db3af7a70a91c54ac35ccb246ba393a"}