{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CK25TDPXUUURORGR5HAUICZY6G","short_pith_number":"pith:CK25TDPX","schema_version":"1.0","canonical_sha256":"12b5d98df7a5291744d1e9c1440b38f1a835f70c3bd1b62e2c87d3720c857a61","source":{"kind":"arxiv","id":"1401.1966","version":1},"attestation_state":"computed","paper":{"title":"The Finsler Metric Obtained as the $\\Gamma$-limit of a Generalised Manhattan Metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel C. Sutton, Hartmut Schwetlick, Johannes Zimmer","submitted_at":"2014-01-09T11:49:56Z","abstract_excerpt":"The $\\Gamma$-limit for a sequence of length functionals associated with a one parameter family of Riemannian manifolds is computed analytically. The Riemannian manifold is of `two-phase' type, that is, the metric coefficient takes values in $\\{1,\\beta\\}$, with $\\beta$ sufficiently large. The metric coefficient takes the value $\\beta$ on squares, the size of which are controlled by a single parameter. We find a family of examples of limiting Finsler metrics that are piecewise affine with infinitely many lines of discontinuity. Such an example provides insight into how the limit metric behaves u"},"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":"1401.1966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-09T11:49:56Z","cross_cats_sorted":[],"title_canon_sha256":"6a8c1ecde93ae6e4833e05fba1525f11868c0898bff341cfc4aeec2401bec532","abstract_canon_sha256":"3345e774945518677725e945355b1ea8cc28fcf4c58305b809b5ba5a9105bca1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:56.095405Z","signature_b64":"FiXHJZDZuylSR+AwBsfrYkdf6r4g8S9N/N+7a5RgAPcHDuPSFZE/REdjIwu5uMgySqXyI+e88v6Md6NT9SqdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b5d98df7a5291744d1e9c1440b38f1a835f70c3bd1b62e2c87d3720c857a61","last_reissued_at":"2026-05-18T03:02:56.094898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:56.094898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Finsler Metric Obtained as the $\\Gamma$-limit of a Generalised Manhattan Metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel C. Sutton, Hartmut Schwetlick, Johannes Zimmer","submitted_at":"2014-01-09T11:49:56Z","abstract_excerpt":"The $\\Gamma$-limit for a sequence of length functionals associated with a one parameter family of Riemannian manifolds is computed analytically. The Riemannian manifold is of `two-phase' type, that is, the metric coefficient takes values in $\\{1,\\beta\\}$, with $\\beta$ sufficiently large. The metric coefficient takes the value $\\beta$ on squares, the size of which are controlled by a single parameter. We find a family of examples of limiting Finsler metrics that are piecewise affine with infinitely many lines of discontinuity. Such an example provides insight into how the limit metric behaves u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1966","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":"1401.1966","created_at":"2026-05-18T03:02:56.094983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.1966v1","created_at":"2026-05-18T03:02:56.094983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1966","created_at":"2026-05-18T03:02:56.094983+00:00"},{"alias_kind":"pith_short_12","alias_value":"CK25TDPXUUUR","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CK25TDPXUUURORGR","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CK25TDPX","created_at":"2026-05-18T12:28:22.404517+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/CK25TDPXUUURORGR5HAUICZY6G","json":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G.json","graph_json":"https://pith.science/api/pith-number/CK25TDPXUUURORGR5HAUICZY6G/graph.json","events_json":"https://pith.science/api/pith-number/CK25TDPXUUURORGR5HAUICZY6G/events.json","paper":"https://pith.science/paper/CK25TDPX"},"agent_actions":{"view_html":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G","download_json":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G.json","view_paper":"https://pith.science/paper/CK25TDPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.1966&json=true","fetch_graph":"https://pith.science/api/pith-number/CK25TDPXUUURORGR5HAUICZY6G/graph.json","fetch_events":"https://pith.science/api/pith-number/CK25TDPXUUURORGR5HAUICZY6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G/action/storage_attestation","attest_author":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G/action/author_attestation","sign_citation":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G/action/citation_signature","submit_replication":"https://pith.science/pith/CK25TDPXUUURORGR5HAUICZY6G/action/replication_record"}},"created_at":"2026-05-18T03:02:56.094983+00:00","updated_at":"2026-05-18T03:02:56.094983+00:00"}