{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DDTFFM4NX3KYNR5JZY5N2QJY7K","short_pith_number":"pith:DDTFFM4N","canonical_record":{"source":{"id":"1507.03410","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-13T12:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"803d87f2c27c7c17741a2e278f2a9c7ffabbf7450330cd66bf15d6a53096b726","abstract_canon_sha256":"34e62cf2bad9781e481e6ccde98b762645a6515397ae2b42b372e38b08febc57"},"schema_version":"1.0"},"canonical_sha256":"18e652b38dbed586c7a9ce3add4138fa821b780c639e164bae634c7a1abe5788","source":{"kind":"arxiv","id":"1507.03410","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03410","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03410v3","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03410","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"DDTFFM4NX3KY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DDTFFM4NX3KYNR5J","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DDTFFM4N","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DDTFFM4NX3KYNR5JZY5N2QJY7K","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03410","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-13T12:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"803d87f2c27c7c17741a2e278f2a9c7ffabbf7450330cd66bf15d6a53096b726","abstract_canon_sha256":"34e62cf2bad9781e481e6ccde98b762645a6515397ae2b42b372e38b08febc57"},"schema_version":"1.0"},"canonical_sha256":"18e652b38dbed586c7a9ce3add4138fa821b780c639e164bae634c7a1abe5788","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:52.275109Z","signature_b64":"8Ot+unK1wzjcCET6hgr2fNvydAig73MseatxzFk23tzSZGtCCF4HRPhUA6AEIE7aCSUnPYd0BVXEBekde0uDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18e652b38dbed586c7a9ce3add4138fa821b780c639e164bae634c7a1abe5788","last_reissued_at":"2026-05-18T00:55:52.274590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:52.274590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03410","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":"2026-05-18T00:55:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zoqevtklYtm5YbjiMxxR6lw+gjXzOkV41Y61eKDJr8OIvKU79iguPEhW/g5ixjDCHzJPKCWkL48sw/TH3yqADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:39:37.814794Z"},"content_sha256":"dafeb820f44e86653d6c520fb70fa5159cf789401370a1a1bd52bcacfb7d74a9","schema_version":"1.0","event_id":"sha256:dafeb820f44e86653d6c520fb70fa5159cf789401370a1a1bd52bcacfb7d74a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DDTFFM4NX3KYNR5JZY5N2QJY7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Courant-sharp eigenvalues of Neumann 2-rep-tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"David Fajman, Michael Bersudsky, Ram Band","submitted_at":"2015-07-13T12:00:39Z","abstract_excerpt":"We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\\sqrt{2}$ (also known as the A4 paper). In $\\R^{n}$ the domains are boxes which generalize the mentioned planar rectangle. The symmetries of those domains reveal a special structure of their eigenfunctions, which we call folding\\textbackslash{}unfolding. This structure affects the nodal set of the eigenfunctions, which in turn allows to derive necessary conditions for Courant-sharpness. In addition, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03410","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":"2026-05-18T00:55:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nio76/asRm3CmThI8zMzbl9v/MfsDnGhWFptvPY26JZOiAdarlYTaIzR0VyTn84C3IdjcxBvK3hS9lGiRtfvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:39:37.815495Z"},"content_sha256":"99c4568e6d2bb3b75b421b5161256f5cfe507a6b3562056ae48c127b001edd28","schema_version":"1.0","event_id":"sha256:99c4568e6d2bb3b75b421b5161256f5cfe507a6b3562056ae48c127b001edd28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/bundle.json","state_url":"https://pith.science/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/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":"2026-06-11T16:39:37Z","links":{"resolver":"https://pith.science/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K","bundle":"https://pith.science/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/bundle.json","state":"https://pith.science/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDTFFM4NX3KYNR5JZY5N2QJY7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DDTFFM4NX3KYNR5JZY5N2QJY7K","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":"34e62cf2bad9781e481e6ccde98b762645a6515397ae2b42b372e38b08febc57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-13T12:00:39Z","title_canon_sha256":"803d87f2c27c7c17741a2e278f2a9c7ffabbf7450330cd66bf15d6a53096b726"},"schema_version":"1.0","source":{"id":"1507.03410","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03410","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03410v3","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03410","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"DDTFFM4NX3KY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DDTFFM4NX3KYNR5J","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DDTFFM4N","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:99c4568e6d2bb3b75b421b5161256f5cfe507a6b3562056ae48c127b001edd28","target":"graph","created_at":"2026-05-18T00:55:52Z","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":"We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\\sqrt{2}$ (also known as the A4 paper). In $\\R^{n}$ the domains are boxes which generalize the mentioned planar rectangle. The symmetries of those domains reveal a special structure of their eigenfunctions, which we call folding\\textbackslash{}unfolding. This structure affects the nodal set of the eigenfunctions, which in turn allows to derive necessary conditions for Courant-sharpness. In addition, th","authors_text":"David Fajman, Michael Bersudsky, Ram Band","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-13T12:00:39Z","title":"Courant-sharp eigenvalues of Neumann 2-rep-tiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03410","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:dafeb820f44e86653d6c520fb70fa5159cf789401370a1a1bd52bcacfb7d74a9","target":"record","created_at":"2026-05-18T00:55:52Z","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":"34e62cf2bad9781e481e6ccde98b762645a6515397ae2b42b372e38b08febc57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-13T12:00:39Z","title_canon_sha256":"803d87f2c27c7c17741a2e278f2a9c7ffabbf7450330cd66bf15d6a53096b726"},"schema_version":"1.0","source":{"id":"1507.03410","kind":"arxiv","version":3}},"canonical_sha256":"18e652b38dbed586c7a9ce3add4138fa821b780c639e164bae634c7a1abe5788","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e652b38dbed586c7a9ce3add4138fa821b780c639e164bae634c7a1abe5788","first_computed_at":"2026-05-18T00:55:52.274590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:52.274590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Ot+unK1wzjcCET6hgr2fNvydAig73MseatxzFk23tzSZGtCCF4HRPhUA6AEIE7aCSUnPYd0BVXEBekde0uDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:52.275109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03410","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dafeb820f44e86653d6c520fb70fa5159cf789401370a1a1bd52bcacfb7d74a9","sha256:99c4568e6d2bb3b75b421b5161256f5cfe507a6b3562056ae48c127b001edd28"],"state_sha256":"0040cdb704ac0ac0a4bb6590b16f33db93737db51011ccc700fa3cf69685f39c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ltKDd2WAr0Ql/7DCNcAuHR9Cz689K6kFEafpgl751kyIIVFAoyRuTqoiQf+IZi65NWOmsaabY6X3mVmibhkAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:39:37.818909Z","bundle_sha256":"1d18aa08d9ce65ecab2e25dacd4b5ff8e97905d3b52e923bc326c9b04102da2b"}}