{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SWBNOJFQKESCPKN4G7HONIZKTV","short_pith_number":"pith:SWBNOJFQ","canonical_record":{"source":{"id":"1305.6356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-28T03:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"6d1601890bf7e6cf82487fe1ea4bf9f25a122b1cb18a5d5ec5ac1ae31924f135","abstract_canon_sha256":"8fadf7da5dbff3548b8762adc2c2acb36026c450188f951741f97c7f7be0763e"},"schema_version":"1.0"},"canonical_sha256":"9582d724b0512427a9bc37cee6a32a9d79be6aa052c4c6a512ddb2920d42d37a","source":{"kind":"arxiv","id":"1305.6356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6356","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6356v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6356","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"SWBNOJFQKESC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SWBNOJFQKESCPKN4","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SWBNOJFQ","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SWBNOJFQKESCPKN4G7HONIZKTV","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-28T03:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"6d1601890bf7e6cf82487fe1ea4bf9f25a122b1cb18a5d5ec5ac1ae31924f135","abstract_canon_sha256":"8fadf7da5dbff3548b8762adc2c2acb36026c450188f951741f97c7f7be0763e"},"schema_version":"1.0"},"canonical_sha256":"9582d724b0512427a9bc37cee6a32a9d79be6aa052c4c6a512ddb2920d42d37a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:40.958648Z","signature_b64":"1LbsCP5j2GzPCSCObGrWLfVWIiLgl+3owHaN/aV/xNfhdG/DffqhnesyCzYb5MSKQJn2QChze4DXXC6REBUSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9582d724b0512427a9bc37cee6a32a9d79be6aa052c4c6a512ddb2920d42d37a","last_reissued_at":"2026-05-18T03:24:40.957934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:40.957934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6356","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":"2026-05-18T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAjFVxZRH7OumBykrjwpLUKi8b1WeoXMKNAyYokQfdW75HMa7PwpHsbZnc4zoRpDrdUkY8LVXTZC/3AunJGfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:49:08.802616Z"},"content_sha256":"bd6d162f80bafdb86e9683db0c9b6ea9feef089ab2a61dfc132c8772a4c587c5","schema_version":"1.0","event_id":"sha256:bd6d162f80bafdb86e9683db0c9b6ea9feef089ab2a61dfc132c8772a4c587c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SWBNOJFQKESCPKN4G7HONIZKTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sign changes of Fourier coefficients of Eisenstein series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Linowitz, Lola Thompson","submitted_at":"2013-05-28T03:38:49Z","abstract_excerpt":"In this paper we prove a number of theorems that determine the extent to which the signs of the Hecke eigenvalues of an Eisenstein newform determine the newform. We address this problem broadly and provide theorems of both individual and statistical nature. Many of these results are Eisenstein series analogues of well-known theorems for cusp forms. For instance, we determine how often the p-th Fourier coefficients of an Eisenstein newform begin with a fixed sequence of signs \\varepsilon_p = {\\pm 1, 0}. Moreover, we prove the following variant of the strong multiplicity-one theorem: an Eisenste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6356","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":"2026-05-18T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UnS0158ZrXmJrIM7+J97sW5fCpI2T5j07CKHUTmRpS+oJmrzNJnWJj8ASLt6exBO1++MnxUtUjY8ag8xgsSdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:49:08.802956Z"},"content_sha256":"31fadff5068b95195ab237c1bcc42cade33e672ba5440d7ae9d8415786f571a4","schema_version":"1.0","event_id":"sha256:31fadff5068b95195ab237c1bcc42cade33e672ba5440d7ae9d8415786f571a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWBNOJFQKESCPKN4G7HONIZKTV/bundle.json","state_url":"https://pith.science/pith/SWBNOJFQKESCPKN4G7HONIZKTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWBNOJFQKESCPKN4G7HONIZKTV/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":"2026-06-24T04:49:08Z","links":{"resolver":"https://pith.science/pith/SWBNOJFQKESCPKN4G7HONIZKTV","bundle":"https://pith.science/pith/SWBNOJFQKESCPKN4G7HONIZKTV/bundle.json","state":"https://pith.science/pith/SWBNOJFQKESCPKN4G7HONIZKTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWBNOJFQKESCPKN4G7HONIZKTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SWBNOJFQKESCPKN4G7HONIZKTV","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":"8fadf7da5dbff3548b8762adc2c2acb36026c450188f951741f97c7f7be0763e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-28T03:38:49Z","title_canon_sha256":"6d1601890bf7e6cf82487fe1ea4bf9f25a122b1cb18a5d5ec5ac1ae31924f135"},"schema_version":"1.0","source":{"id":"1305.6356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6356","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6356v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6356","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"SWBNOJFQKESC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SWBNOJFQKESCPKN4","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SWBNOJFQ","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:31fadff5068b95195ab237c1bcc42cade33e672ba5440d7ae9d8415786f571a4","target":"graph","created_at":"2026-05-18T03:24:40Z","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 prove a number of theorems that determine the extent to which the signs of the Hecke eigenvalues of an Eisenstein newform determine the newform. We address this problem broadly and provide theorems of both individual and statistical nature. Many of these results are Eisenstein series analogues of well-known theorems for cusp forms. For instance, we determine how often the p-th Fourier coefficients of an Eisenstein newform begin with a fixed sequence of signs \\varepsilon_p = {\\pm 1, 0}. Moreover, we prove the following variant of the strong multiplicity-one theorem: an Eisenste","authors_text":"Benjamin Linowitz, Lola Thompson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-28T03:38:49Z","title":"The sign changes of Fourier coefficients of Eisenstein series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6356","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:bd6d162f80bafdb86e9683db0c9b6ea9feef089ab2a61dfc132c8772a4c587c5","target":"record","created_at":"2026-05-18T03:24:40Z","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":"8fadf7da5dbff3548b8762adc2c2acb36026c450188f951741f97c7f7be0763e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-28T03:38:49Z","title_canon_sha256":"6d1601890bf7e6cf82487fe1ea4bf9f25a122b1cb18a5d5ec5ac1ae31924f135"},"schema_version":"1.0","source":{"id":"1305.6356","kind":"arxiv","version":1}},"canonical_sha256":"9582d724b0512427a9bc37cee6a32a9d79be6aa052c4c6a512ddb2920d42d37a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9582d724b0512427a9bc37cee6a32a9d79be6aa052c4c6a512ddb2920d42d37a","first_computed_at":"2026-05-18T03:24:40.957934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:40.957934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LbsCP5j2GzPCSCObGrWLfVWIiLgl+3owHaN/aV/xNfhdG/DffqhnesyCzYb5MSKQJn2QChze4DXXC6REBUSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:40.958648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd6d162f80bafdb86e9683db0c9b6ea9feef089ab2a61dfc132c8772a4c587c5","sha256:31fadff5068b95195ab237c1bcc42cade33e672ba5440d7ae9d8415786f571a4"],"state_sha256":"80452df0866f4232a589489783ecdc216d476e57bf6c8ad110b1284563ebf28f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+Ij/0aVTDE5iC3vwqVagUYypWSbypOZMx2WXP7d9A8Hvk9jDl5lHQrXzEumSD+IliSi3NC1qXvEiNGq/oLMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:49:08.805219Z","bundle_sha256":"044315f3cdd2aef68c25162983b56cde6609b0d827074d07eac8a17e0c27b3d7"}}