{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RKPJWH4WCB76HFDLZKUIQ7JFH3","short_pith_number":"pith:RKPJWH4W","canonical_record":{"source":{"id":"1701.02793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T21:40:46Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"41a08d209d90ad33dd67cdaf803d60fddcb95a46cd5791d64b26a2ec0df45a08","abstract_canon_sha256":"5b796e5191d1af0e94a906d0c08f8a9dcf2b9822f08f851c71492a7c62ae1962"},"schema_version":"1.0"},"canonical_sha256":"8a9e9b1f96107fe3946bcaa8887d253ef2b9c229ef6e0efa4ec14a944555b874","source":{"kind":"arxiv","id":"1701.02793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02793","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02793v1","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02793","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"pith_short_12","alias_value":"RKPJWH4WCB76","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKPJWH4WCB76HFDL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKPJWH4W","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RKPJWH4WCB76HFDLZKUIQ7JFH3","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T21:40:46Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"41a08d209d90ad33dd67cdaf803d60fddcb95a46cd5791d64b26a2ec0df45a08","abstract_canon_sha256":"5b796e5191d1af0e94a906d0c08f8a9dcf2b9822f08f851c71492a7c62ae1962"},"schema_version":"1.0"},"canonical_sha256":"8a9e9b1f96107fe3946bcaa8887d253ef2b9c229ef6e0efa4ec14a944555b874","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:00.154742Z","signature_b64":"T/8YnVzx4zlbBYezHZyZ8zXOt9JL/oUqiHNwhnsLc2XkdeofxLOJID78VLikrIrERBXJ+vxwwVO8Rv0HvjXeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a9e9b1f96107fe3946bcaa8887d253ef2b9c229ef6e0efa4ec14a944555b874","last_reissued_at":"2026-05-18T00:53:00.154134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:00.154134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02793","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8MoZzTA3NHUn14+wacj15RRKQRJeNRNfEIW/ToIX+1QOd7dHhlzLvDk6VtktbASWGjvr8d9c44iUZHoX7gxeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:56:05.191088Z"},"content_sha256":"4666f021b4d7452e8a308013cd33fee66ffcedeb6ae82d1b7e51e8022fc1c1cf","schema_version":"1.0","event_id":"sha256:4666f021b4d7452e8a308013cd33fee66ffcedeb6ae82d1b7e51e8022fc1c1cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RKPJWH4WCB76HFDLZKUIQ7JFH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution of Neumann data mass on triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Hans Christianson","submitted_at":"2017-01-10T21:40:46Z","abstract_excerpt":"In this paper we study the behaviour of the Neumann data of Dirichlet eigenfunctions on triangles. We prove that the $L^2$ norm of the (semi-classical) Neumann data on each side is equal to the length of the side divided by the area of the triangle. The novel feature of this result is that it is {\\it not} an asymptotic, but an exact formula. The proof is by simple integrations by parts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02793","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ELFE98c58YlgoD4iJPcMqfo9SQmIL2idy/UKbKsak1IANKkioabeLQGb4EZLoOAHp4K27iNbOAjCZFY5PHCnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:56:05.191440Z"},"content_sha256":"85ec7730e2f879ab0f4135cafad71cbbf9746a00e4cc6baa640a7766f52ab1a2","schema_version":"1.0","event_id":"sha256:85ec7730e2f879ab0f4135cafad71cbbf9746a00e4cc6baa640a7766f52ab1a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/bundle.json","state_url":"https://pith.science/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/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":"2026-06-24T23:56:05Z","links":{"resolver":"https://pith.science/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3","bundle":"https://pith.science/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/bundle.json","state":"https://pith.science/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKPJWH4WCB76HFDLZKUIQ7JFH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RKPJWH4WCB76HFDLZKUIQ7JFH3","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":"5b796e5191d1af0e94a906d0c08f8a9dcf2b9822f08f851c71492a7c62ae1962","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T21:40:46Z","title_canon_sha256":"41a08d209d90ad33dd67cdaf803d60fddcb95a46cd5791d64b26a2ec0df45a08"},"schema_version":"1.0","source":{"id":"1701.02793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02793","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02793v1","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02793","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"pith_short_12","alias_value":"RKPJWH4WCB76","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKPJWH4WCB76HFDL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKPJWH4W","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:85ec7730e2f879ab0f4135cafad71cbbf9746a00e4cc6baa640a7766f52ab1a2","target":"graph","created_at":"2026-05-18T00:53:00Z","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":"In this paper we study the behaviour of the Neumann data of Dirichlet eigenfunctions on triangles. We prove that the $L^2$ norm of the (semi-classical) Neumann data on each side is equal to the length of the side divided by the area of the triangle. The novel feature of this result is that it is {\\it not} an asymptotic, but an exact formula. The proof is by simple integrations by parts.","authors_text":"Hans Christianson","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T21:40:46Z","title":"Equidistribution of Neumann data mass on triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02793","kind":"arxiv","version":1},"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":"sha256:4666f021b4d7452e8a308013cd33fee66ffcedeb6ae82d1b7e51e8022fc1c1cf","target":"record","created_at":"2026-05-18T00:53:00Z","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":"5b796e5191d1af0e94a906d0c08f8a9dcf2b9822f08f851c71492a7c62ae1962","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T21:40:46Z","title_canon_sha256":"41a08d209d90ad33dd67cdaf803d60fddcb95a46cd5791d64b26a2ec0df45a08"},"schema_version":"1.0","source":{"id":"1701.02793","kind":"arxiv","version":1}},"canonical_sha256":"8a9e9b1f96107fe3946bcaa8887d253ef2b9c229ef6e0efa4ec14a944555b874","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a9e9b1f96107fe3946bcaa8887d253ef2b9c229ef6e0efa4ec14a944555b874","first_computed_at":"2026-05-18T00:53:00.154134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:00.154134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/8YnVzx4zlbBYezHZyZ8zXOt9JL/oUqiHNwhnsLc2XkdeofxLOJID78VLikrIrERBXJ+vxwwVO8Rv0HvjXeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:00.154742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4666f021b4d7452e8a308013cd33fee66ffcedeb6ae82d1b7e51e8022fc1c1cf","sha256:85ec7730e2f879ab0f4135cafad71cbbf9746a00e4cc6baa640a7766f52ab1a2"],"state_sha256":"01665ba5e4d84cc45286979509a5474a9efd846f90797dcc4d9e88f22fdb5147"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsUh9y+14Dm6QigqysBshkwc3+4Hs1wkmdDGtzrC2CJPMbKu88euCB8on1j0Dkfv382cSlhHgQs4R0jhQxIfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:56:05.193311Z","bundle_sha256":"4aa7a1e749ef436ef38fe82abc763db76bfc727f4cb525ba1db730c9da9cc976"}}