{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3K62NI2IPS5O3O77XXNZ2IO6BZ","short_pith_number":"pith:3K62NI2I","canonical_record":{"source":{"id":"1803.08311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:32:11Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"e61fb7f932acd430ac53d41f10d1c1ec1c8e48577d2e91cf8a5e596699d02481","abstract_canon_sha256":"df06f33aa459bc6af7de2016b272bb9e6ce8df1b89432cb8c031cc6c76cfd121"},"schema_version":"1.0"},"canonical_sha256":"dabda6a3487cbaedbbffbddb9d21de0e7d78d75dd5540af590ffcb4a86c6a57e","source":{"kind":"arxiv","id":"1803.08311","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08311","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08311v2","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08311","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"3K62NI2IPS5O","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3K62NI2IPS5O3O77","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3K62NI2I","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3K62NI2IPS5O3O77XXNZ2IO6BZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:32:11Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"e61fb7f932acd430ac53d41f10d1c1ec1c8e48577d2e91cf8a5e596699d02481","abstract_canon_sha256":"df06f33aa459bc6af7de2016b272bb9e6ce8df1b89432cb8c031cc6c76cfd121"},"schema_version":"1.0"},"canonical_sha256":"dabda6a3487cbaedbbffbddb9d21de0e7d78d75dd5540af590ffcb4a86c6a57e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:59.178829Z","signature_b64":"rdwTwQ00etY0A21leVzhbBb9smAv6HpSYiU2kP+8NPKbcSg2bKa2TP/14UTX8UDdxaPd30lphrd576gueL7tBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dabda6a3487cbaedbbffbddb9d21de0e7d78d75dd5540af590ffcb4a86c6a57e","last_reissued_at":"2026-05-18T00:04:59.178335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:59.178335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08311","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":"2026-05-18T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+AmApHVFldC35L9gg6ZajCNFFvSEt035Gc3Ac7gYFGrRIMufiusmeZQxhcaBCVziiaSzD3GZNjjsHWRDyXHHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:24:28.762170Z"},"content_sha256":"a4d039a4b1ed0d4874a4b6192ba0fdc1fbe9d973b52cfc9d145d29baa9c8ce3a","schema_version":"1.0","event_id":"sha256:a4d039a4b1ed0d4874a4b6192ba0fdc1fbe9d973b52cfc9d145d29baa9c8ce3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3K62NI2IPS5O3O77XXNZ2IO6BZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal scarring for eigenfunctions of quantum graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Brian Winn, Gregory Berkolaiko","submitted_at":"2018-03-22T11:32:11Z","abstract_excerpt":"We prove the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits back-scattering. We prove the existence of scars that are half-delocalised on a single bond. Moreover we show that the scarred states we construct are maximal in the sense that it is impossible to have quantum eigenfunctions with a significantly lower entropy than our examples.\n  These scarred eigenstates are on graphs that exhibit generic spectral statistics of random matrix type in the large graph limit, and, in c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08311","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":"2026-05-18T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dmq0tCG1C8WoFq8MOzm4hbAXvvQgFGpnAZvNL9FZAokDAbpDXw38eOEEII1EcUsWdV4hs2WQqPcJzQCxUqwJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:24:28.762538Z"},"content_sha256":"40735b85501bf1da6084f69fff2eb43ed169c9889193a88c02bbce94e79613a5","schema_version":"1.0","event_id":"sha256:40735b85501bf1da6084f69fff2eb43ed169c9889193a88c02bbce94e79613a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/bundle.json","state_url":"https://pith.science/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/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":"2026-06-22T23:24:28Z","links":{"resolver":"https://pith.science/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ","bundle":"https://pith.science/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/bundle.json","state":"https://pith.science/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3K62NI2IPS5O3O77XXNZ2IO6BZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3K62NI2IPS5O3O77XXNZ2IO6BZ","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":"df06f33aa459bc6af7de2016b272bb9e6ce8df1b89432cb8c031cc6c76cfd121","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:32:11Z","title_canon_sha256":"e61fb7f932acd430ac53d41f10d1c1ec1c8e48577d2e91cf8a5e596699d02481"},"schema_version":"1.0","source":{"id":"1803.08311","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08311","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08311v2","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08311","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"3K62NI2IPS5O","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3K62NI2IPS5O3O77","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3K62NI2I","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:40735b85501bf1da6084f69fff2eb43ed169c9889193a88c02bbce94e79613a5","target":"graph","created_at":"2026-05-18T00:04:59Z","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 the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits back-scattering. We prove the existence of scars that are half-delocalised on a single bond. Moreover we show that the scarred states we construct are maximal in the sense that it is impossible to have quantum eigenfunctions with a significantly lower entropy than our examples.\n  These scarred eigenstates are on graphs that exhibit generic spectral statistics of random matrix type in the large graph limit, and, in c","authors_text":"Brian Winn, Gregory Berkolaiko","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:32:11Z","title":"Maximal scarring for eigenfunctions of quantum graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08311","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:a4d039a4b1ed0d4874a4b6192ba0fdc1fbe9d973b52cfc9d145d29baa9c8ce3a","target":"record","created_at":"2026-05-18T00:04:59Z","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":"df06f33aa459bc6af7de2016b272bb9e6ce8df1b89432cb8c031cc6c76cfd121","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:32:11Z","title_canon_sha256":"e61fb7f932acd430ac53d41f10d1c1ec1c8e48577d2e91cf8a5e596699d02481"},"schema_version":"1.0","source":{"id":"1803.08311","kind":"arxiv","version":2}},"canonical_sha256":"dabda6a3487cbaedbbffbddb9d21de0e7d78d75dd5540af590ffcb4a86c6a57e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dabda6a3487cbaedbbffbddb9d21de0e7d78d75dd5540af590ffcb4a86c6a57e","first_computed_at":"2026-05-18T00:04:59.178335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:59.178335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdwTwQ00etY0A21leVzhbBb9smAv6HpSYiU2kP+8NPKbcSg2bKa2TP/14UTX8UDdxaPd30lphrd576gueL7tBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:59.178829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08311","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4d039a4b1ed0d4874a4b6192ba0fdc1fbe9d973b52cfc9d145d29baa9c8ce3a","sha256:40735b85501bf1da6084f69fff2eb43ed169c9889193a88c02bbce94e79613a5"],"state_sha256":"5869206aaf736a9bfd048b80f0ed43d0f226a714aecdff6933e5dc4e5f2950ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfqTOTBJkj6Sf6N+a4s5lPu4vMM6uUE3DF1ZeYIWPuGqXy3Ld2WLhmaoDYtQWmtr8Z2iwFz5OLAeHF71Oe4DCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:24:28.764588Z","bundle_sha256":"fd030cb896ea9aefecac1549ddea60138401cd128fbcdfc64a81dcae64114cc7"}}