{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TDNP4LLDEHRT7MYIB3HZW2GYRX","short_pith_number":"pith:TDNP4LLD","canonical_record":{"source":{"id":"1601.04999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T17:04:22Z","cross_cats_sorted":[],"title_canon_sha256":"c5355d06a50b2cbd19ae1b0591beb0f68e62fcb7e174c0c4c5c3495343a803e3","abstract_canon_sha256":"20013b92050ecc1d88d3a9d5384cd0d8819e1bf7965d0f4d30e39035aaad1fa1"},"schema_version":"1.0"},"canonical_sha256":"98dafe2d6321e33fb3080ecf9b68d88dc08eae6e9bd7e254f67a403c88657ca4","source":{"kind":"arxiv","id":"1601.04999","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04999","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04999v2","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04999","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"TDNP4LLDEHRT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDNP4LLDEHRT7MYI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDNP4LLD","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TDNP4LLDEHRT7MYIB3HZW2GYRX","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T17:04:22Z","cross_cats_sorted":[],"title_canon_sha256":"c5355d06a50b2cbd19ae1b0591beb0f68e62fcb7e174c0c4c5c3495343a803e3","abstract_canon_sha256":"20013b92050ecc1d88d3a9d5384cd0d8819e1bf7965d0f4d30e39035aaad1fa1"},"schema_version":"1.0"},"canonical_sha256":"98dafe2d6321e33fb3080ecf9b68d88dc08eae6e9bd7e254f67a403c88657ca4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.705694Z","signature_b64":"bj9pbQJOipm3ZNNZJ1qno4QMy6MZRI2F1vesIoLesmw0p5gSQk3YFasPeMIIHdyLMjO2D02FfMKpMDtlXJYMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98dafe2d6321e33fb3080ecf9b68d88dc08eae6e9bd7e254f67a403c88657ca4","last_reissued_at":"2026-05-18T00:10:19.704995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.704995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04999","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":"2026-05-18T00:10:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGRpfkPGvkMGKprKI/GSJikMu0oKXNNBSHT+2gumhVErOZeDf6u22pDRdddoSoSAE7f86QyfxpONz503j6u1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:28:18.830058Z"},"content_sha256":"48da08be6f234e040af6d034d8464b658a11cd50a31b98ca8923e98a64cb9d74","schema_version":"1.0","event_id":"sha256:48da08be6f234e040af6d034d8464b658a11cd50a31b98ca8923e98a64cb9d74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TDNP4LLDEHRT7MYIB3HZW2GYRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional equations for multi-signed Selmer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Lei, Gautier Ponsinet","submitted_at":"2016-01-19T17:04:22Z","abstract_excerpt":"We study the functional equation for the multi-signed Selmer groups for non-ordinary motives whose Hodge-Tate weights are $0$ and $1$, defined by B\\\"uy\\\"ukboduk and the first named author. This generalizes simultaneously Greenberg's result for ordinary motives and Kim's result for supersingular elliptic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04999","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":"2026-05-18T00:10:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EobUD0kh2zcayB0aQjupk2GMTTDdhFi4itXF6sxIpAlTVf/McbBLkITeQxx89T/UQuRVD/DJKe1wxPs1Zv0uDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:28:18.830528Z"},"content_sha256":"2d635bb6fc269a4143950a9a957df0344db596e8770bece5dd6c18cf314f4d05","schema_version":"1.0","event_id":"sha256:2d635bb6fc269a4143950a9a957df0344db596e8770bece5dd6c18cf314f4d05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/bundle.json","state_url":"https://pith.science/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/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":"2026-07-01T20:28:18Z","links":{"resolver":"https://pith.science/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX","bundle":"https://pith.science/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/bundle.json","state":"https://pith.science/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDNP4LLDEHRT7MYIB3HZW2GYRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TDNP4LLDEHRT7MYIB3HZW2GYRX","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":"20013b92050ecc1d88d3a9d5384cd0d8819e1bf7965d0f4d30e39035aaad1fa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T17:04:22Z","title_canon_sha256":"c5355d06a50b2cbd19ae1b0591beb0f68e62fcb7e174c0c4c5c3495343a803e3"},"schema_version":"1.0","source":{"id":"1601.04999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04999","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04999v2","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04999","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"TDNP4LLDEHRT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDNP4LLDEHRT7MYI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDNP4LLD","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2d635bb6fc269a4143950a9a957df0344db596e8770bece5dd6c18cf314f4d05","target":"graph","created_at":"2026-05-18T00:10:19Z","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 study the functional equation for the multi-signed Selmer groups for non-ordinary motives whose Hodge-Tate weights are $0$ and $1$, defined by B\\\"uy\\\"ukboduk and the first named author. This generalizes simultaneously Greenberg's result for ordinary motives and Kim's result for supersingular elliptic curves.","authors_text":"Antonio Lei, Gautier Ponsinet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T17:04:22Z","title":"Functional equations for multi-signed Selmer groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04999","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":"sha256:48da08be6f234e040af6d034d8464b658a11cd50a31b98ca8923e98a64cb9d74","target":"record","created_at":"2026-05-18T00:10:19Z","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":"20013b92050ecc1d88d3a9d5384cd0d8819e1bf7965d0f4d30e39035aaad1fa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T17:04:22Z","title_canon_sha256":"c5355d06a50b2cbd19ae1b0591beb0f68e62fcb7e174c0c4c5c3495343a803e3"},"schema_version":"1.0","source":{"id":"1601.04999","kind":"arxiv","version":2}},"canonical_sha256":"98dafe2d6321e33fb3080ecf9b68d88dc08eae6e9bd7e254f67a403c88657ca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98dafe2d6321e33fb3080ecf9b68d88dc08eae6e9bd7e254f67a403c88657ca4","first_computed_at":"2026-05-18T00:10:19.704995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:19.704995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bj9pbQJOipm3ZNNZJ1qno4QMy6MZRI2F1vesIoLesmw0p5gSQk3YFasPeMIIHdyLMjO2D02FfMKpMDtlXJYMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:19.705694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48da08be6f234e040af6d034d8464b658a11cd50a31b98ca8923e98a64cb9d74","sha256:2d635bb6fc269a4143950a9a957df0344db596e8770bece5dd6c18cf314f4d05"],"state_sha256":"11d05865ed11210c1a31d5e473db4c34831429ed1c6a12a671338da9b6b23e07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ibz3j9Z2Nf6NzIpxdkuVl2DVYwmY8J3AEqvU+dMgYS6VEmH8q74Zqaj6Hjeemn0INmA6Wdq4TEIG3szfAdwLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T20:28:18.832558Z","bundle_sha256":"d7c00adb1fb35a52a8222e743af3b74c81e3fdcce579f1d9b99e7e99394e3cfb"}}