{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4SUJOQZLY3PGZUVPY3DVLNBJIN","short_pith_number":"pith:4SUJOQZL","canonical_record":{"source":{"id":"1609.07408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T15:50:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9dd999afafa87322c1860f60c42251d1c3169a0c78eda5aecb3965482ed8a7e7","abstract_canon_sha256":"fcd55c0c3c308e698a202552404d604c7eea352c0487dddaac8e9a001695bf24"},"schema_version":"1.0"},"canonical_sha256":"e4a897432bc6de6cd2afc6c755b4294364379f194b337ec988e60b28b6285d95","source":{"kind":"arxiv","id":"1609.07408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07408","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07408v2","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07408","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"4SUJOQZLY3PG","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4SUJOQZLY3PGZUVP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4SUJOQZL","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4SUJOQZLY3PGZUVPY3DVLNBJIN","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T15:50:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9dd999afafa87322c1860f60c42251d1c3169a0c78eda5aecb3965482ed8a7e7","abstract_canon_sha256":"fcd55c0c3c308e698a202552404d604c7eea352c0487dddaac8e9a001695bf24"},"schema_version":"1.0"},"canonical_sha256":"e4a897432bc6de6cd2afc6c755b4294364379f194b337ec988e60b28b6285d95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:15.767960Z","signature_b64":"9l3UZcAI4e8MvpFUArHRyWjGsB5YwOZBViu+oHgdebefDDhVjxS6kqT1ohBBnyM9jO1abl/BMyiBIDFNw7ISAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a897432bc6de6cd2afc6c755b4294364379f194b337ec988e60b28b6285d95","last_reissued_at":"2026-05-18T00:34:15.767362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:15.767362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07408","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYDn4jR39MRzUwH9T+tbV5nQbIkzJO91OM/o9YsG1mIi74xluEJMd+pAPRB4Ryy2quSUEZSFSDMJ9vVAAw+3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:13:53.799983Z"},"content_sha256":"63413e9955843e9e6efc2675c71803b87f9ca173781858ec4215ef2c2853062f","schema_version":"1.0","event_id":"sha256:63413e9955843e9e6efc2675c71803b87f9ca173781858ec4215ef2c2853062f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4SUJOQZLY3PGZUVPY3DVLNBJIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Martin Tautenhahn, Matthias T\\\"aufer","submitted_at":"2016-09-23T15:50:58Z","abstract_excerpt":"We prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schr\\\"odinger operators. Let $\\Lambda_L = (-L/2,L/2)^d$ and $H_L = -\\Delta_L + V_L$ be a Schr\\\"odinger operator on $L^2 (\\Lambda_L)$ with a bounded potential $V_L : \\Lambda_L \\to \\mathbb{R}^d$ and Dirichlet, Neumann, or periodic boundary conditions. Our main result is of the type\n  \\[\n  \\int_{\\Lambda_L} \\lvert \\phi \\rvert^2 \\leq C_{\\mathrm{sfuc}} \\int_{W_\\delta (L)} \\lvert \\phi \\rvert^2,\n  \\] where $\\phi$ is an infinite complex linear combination of eigenfunctions of $H_L$ with exponentially de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07408","kind":"arxiv","version":2},"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":"2026-05-18T00:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kv3N1G2zJylD96yflpgAApwx8a/eOp0pJBe23+fZhvPAyBKl9f0O8wwNcvKzglUOE6ZXFpi5geexohuqcOdxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:13:53.800386Z"},"content_sha256":"8139e35d4cd9fdf173a9198e817ae4e7b3620a75fb74f35289c0ac050b48540c","schema_version":"1.0","event_id":"sha256:8139e35d4cd9fdf173a9198e817ae4e7b3620a75fb74f35289c0ac050b48540c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/bundle.json","state_url":"https://pith.science/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/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":"2026-06-23T21:13:53Z","links":{"resolver":"https://pith.science/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN","bundle":"https://pith.science/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/bundle.json","state":"https://pith.science/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SUJOQZLY3PGZUVPY3DVLNBJIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4SUJOQZLY3PGZUVPY3DVLNBJIN","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":"fcd55c0c3c308e698a202552404d604c7eea352c0487dddaac8e9a001695bf24","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T15:50:58Z","title_canon_sha256":"9dd999afafa87322c1860f60c42251d1c3169a0c78eda5aecb3965482ed8a7e7"},"schema_version":"1.0","source":{"id":"1609.07408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07408","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07408v2","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07408","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"4SUJOQZLY3PG","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4SUJOQZLY3PGZUVP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4SUJOQZL","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:8139e35d4cd9fdf173a9198e817ae4e7b3620a75fb74f35289c0ac050b48540c","target":"graph","created_at":"2026-05-18T00:34:15Z","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 prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schr\\\"odinger operators. Let $\\Lambda_L = (-L/2,L/2)^d$ and $H_L = -\\Delta_L + V_L$ be a Schr\\\"odinger operator on $L^2 (\\Lambda_L)$ with a bounded potential $V_L : \\Lambda_L \\to \\mathbb{R}^d$ and Dirichlet, Neumann, or periodic boundary conditions. Our main result is of the type\n  \\[\n  \\int_{\\Lambda_L} \\lvert \\phi \\rvert^2 \\leq C_{\\mathrm{sfuc}} \\int_{W_\\delta (L)} \\lvert \\phi \\rvert^2,\n  \\] where $\\phi$ is an infinite complex linear combination of eigenfunctions of $H_L$ with exponentially de","authors_text":"Martin Tautenhahn, Matthias T\\\"aufer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T15:50:58Z","title":"Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07408","kind":"arxiv","version":2},"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":"sha256:63413e9955843e9e6efc2675c71803b87f9ca173781858ec4215ef2c2853062f","target":"record","created_at":"2026-05-18T00:34:15Z","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":"fcd55c0c3c308e698a202552404d604c7eea352c0487dddaac8e9a001695bf24","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T15:50:58Z","title_canon_sha256":"9dd999afafa87322c1860f60c42251d1c3169a0c78eda5aecb3965482ed8a7e7"},"schema_version":"1.0","source":{"id":"1609.07408","kind":"arxiv","version":2}},"canonical_sha256":"e4a897432bc6de6cd2afc6c755b4294364379f194b337ec988e60b28b6285d95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a897432bc6de6cd2afc6c755b4294364379f194b337ec988e60b28b6285d95","first_computed_at":"2026-05-18T00:34:15.767362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:15.767362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9l3UZcAI4e8MvpFUArHRyWjGsB5YwOZBViu+oHgdebefDDhVjxS6kqT1ohBBnyM9jO1abl/BMyiBIDFNw7ISAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:15.767960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63413e9955843e9e6efc2675c71803b87f9ca173781858ec4215ef2c2853062f","sha256:8139e35d4cd9fdf173a9198e817ae4e7b3620a75fb74f35289c0ac050b48540c"],"state_sha256":"ca1ecf7d8ef99388862139987a384c4141245c9fb93245b44ccc332183a74011"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJjlTfwCyLdcdz1rHof0xp1u1Fu04wnvt8/yKL+/tAyzLeh6kBILpbLSbrRaKtE+89xI2/cZFrla411P+/o8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:13:53.802310Z","bundle_sha256":"180aa80729a3cc509b00557d3d8ecb077944e96ce5bf370b1ab8eb883aac51da"}}