{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5IVKGBBPMBMR6NNXHKAIN47KWK","short_pith_number":"pith:5IVKGBBP","schema_version":"1.0","canonical_sha256":"ea2aa3042f60591f35b73a8086f3eab28eb4bc6f7651734e6e8c89e8edab503a","source":{"kind":"arxiv","id":"1507.06752","version":1},"attestation_state":"computed","paper":{"title":"Log differentiable spaces and manifolds with corners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Samouil Molcho, W. D. Gillam","submitted_at":"2015-07-24T06:31:48Z","abstract_excerpt":"We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating manifolds with corners generalizing recent work of Kottke-Melrose. We give a treatment of the theory of fans, which are to monoids as schemes are to rings. By adapting similar results from logarithmic algebraic geometry, we prove a general result on resolution of toric singularit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.06752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-24T06:31:48Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"843f72f39ef918657323a5223e5097132b0aaa2973466158a2951f34870ad6ec","abstract_canon_sha256":"7acd1f48848fcd639fd5fa5472a67d560ac700b80cb50b339f6038710487da3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:22.472941Z","signature_b64":"qYf3ViYcnZdBc2xRYHj6+Z8z9rgHEK87x8rBUkOQcHUz0tJKclAsGuwDdvpg98hzdp8EGnYdgcurHQcNdvLPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea2aa3042f60591f35b73a8086f3eab28eb4bc6f7651734e6e8c89e8edab503a","last_reissued_at":"2026-05-18T01:36:22.472286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:22.472286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Log differentiable spaces and manifolds with corners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Samouil Molcho, W. D. Gillam","submitted_at":"2015-07-24T06:31:48Z","abstract_excerpt":"We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating manifolds with corners generalizing recent work of Kottke-Melrose. We give a treatment of the theory of fans, which are to monoids as schemes are to rings. By adapting similar results from logarithmic algebraic geometry, we prove a general result on resolution of toric singularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06752","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.06752","created_at":"2026-05-18T01:36:22.472391+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06752v1","created_at":"2026-05-18T01:36:22.472391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06752","created_at":"2026-05-18T01:36:22.472391+00:00"},{"alias_kind":"pith_short_12","alias_value":"5IVKGBBPMBMR","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5IVKGBBPMBMR6NNX","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5IVKGBBP","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK","json":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK.json","graph_json":"https://pith.science/api/pith-number/5IVKGBBPMBMR6NNXHKAIN47KWK/graph.json","events_json":"https://pith.science/api/pith-number/5IVKGBBPMBMR6NNXHKAIN47KWK/events.json","paper":"https://pith.science/paper/5IVKGBBP"},"agent_actions":{"view_html":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK","download_json":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK.json","view_paper":"https://pith.science/paper/5IVKGBBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06752&json=true","fetch_graph":"https://pith.science/api/pith-number/5IVKGBBPMBMR6NNXHKAIN47KWK/graph.json","fetch_events":"https://pith.science/api/pith-number/5IVKGBBPMBMR6NNXHKAIN47KWK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK/action/storage_attestation","attest_author":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK/action/author_attestation","sign_citation":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK/action/citation_signature","submit_replication":"https://pith.science/pith/5IVKGBBPMBMR6NNXHKAIN47KWK/action/replication_record"}},"created_at":"2026-05-18T01:36:22.472391+00:00","updated_at":"2026-05-18T01:36:22.472391+00:00"}