{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TFXKNQSSND7ATUROOWIPTRHHRX","short_pith_number":"pith:TFXKNQSS","canonical_record":{"source":{"id":"2101.08718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2021-01-21T16:57:33Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"da370f91d09b9e0375556b2b56c3a4a92d8c205528bab974364e8f4e477499c9","abstract_canon_sha256":"3d00fdbfa467c0c37f96ba5e473125b94ab67f855ba4ad71732ea5d54d82e568"},"schema_version":"1.0"},"canonical_sha256":"996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85","source":{"kind":"arxiv","id":"2101.08718","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.08718","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"arxiv_version","alias_value":"2101.08718v2","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.08718","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_12","alias_value":"TFXKNQSSND7A","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_16","alias_value":"TFXKNQSSND7ATURO","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_8","alias_value":"TFXKNQSS","created_at":"2026-07-05T02:43:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TFXKNQSSND7ATUROOWIPTRHHRX","target":"record","payload":{"canonical_record":{"source":{"id":"2101.08718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2021-01-21T16:57:33Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"da370f91d09b9e0375556b2b56c3a4a92d8c205528bab974364e8f4e477499c9","abstract_canon_sha256":"3d00fdbfa467c0c37f96ba5e473125b94ab67f855ba4ad71732ea5d54d82e568"},"schema_version":"1.0"},"canonical_sha256":"996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:43:32.504042Z","signature_b64":"JSjMwpIQWRo/Aw8sJnp4RfHO3b3KAbWAHeqcEI2loou98CI0bwyKKZB043F0wHF789QmTk77UsJnmKmmiNWKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85","last_reissued_at":"2026-07-05T02:43:32.503261Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:43:32.503261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.08718","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":"2026-07-05T02:43:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XIAi3WHLlest1wbtXMNbOIbAdN4Wrm0nQfead0JZLCYPkV/jt/jDOr9EUxWWsnPT0vvedK8nPYc2Z7Am6NHOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:01:10.783683Z"},"content_sha256":"f666a98d5b50393537e1f3729d9ec9a5b99082c4dac3e8c77eebc8613664d2c2","schema_version":"1.0","event_id":"sha256:f666a98d5b50393537e1f3729d9ec9a5b99082c4dac3e8c77eebc8613664d2c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TFXKNQSSND7ATUROOWIPTRHHRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular Invariant Dynamics and Fermion Mass Hierarchies around $\\tau = i$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Andrea Romanino, Arsenii Titov, Ferruccio Feruglio, Valerio Gherardi","submitted_at":"2021-01-21T16:57:33Z","abstract_excerpt":"We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point $\\tau=i$, where modular invariant theories possess a residual $Z_4$ invariance. In this region the breaking of $Z_4$ can be fully described by the spurion $\\epsilon \\approx \\tau - i$, that flips its sign under $Z_4$. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the $Z_4$ symmetry at $\\tau=i$, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of $|\\epsilon|$. We present examples where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.08718","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.08718/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:43:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0efwDFQeIj/5G9I7AVMxo8Cg1lmc1B3ojEICutHwRlevG0mjqh9PeqRLu3tdKKIuK+cmSAUtMcYlZGNkTwSZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:01:10.784014Z"},"content_sha256":"add9d9efe5c1872350de511e5603d87d5beeb8cb00b1b000b5d9a18d7310dccc","schema_version":"1.0","event_id":"sha256:add9d9efe5c1872350de511e5603d87d5beeb8cb00b1b000b5d9a18d7310dccc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFXKNQSSND7ATUROOWIPTRHHRX/bundle.json","state_url":"https://pith.science/pith/TFXKNQSSND7ATUROOWIPTRHHRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFXKNQSSND7ATUROOWIPTRHHRX/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":"2026-08-11T10:01:10Z","links":{"resolver":"https://pith.science/pith/TFXKNQSSND7ATUROOWIPTRHHRX","bundle":"https://pith.science/pith/TFXKNQSSND7ATUROOWIPTRHHRX/bundle.json","state":"https://pith.science/pith/TFXKNQSSND7ATUROOWIPTRHHRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFXKNQSSND7ATUROOWIPTRHHRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TFXKNQSSND7ATUROOWIPTRHHRX","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":"3d00fdbfa467c0c37f96ba5e473125b94ab67f855ba4ad71732ea5d54d82e568","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2021-01-21T16:57:33Z","title_canon_sha256":"da370f91d09b9e0375556b2b56c3a4a92d8c205528bab974364e8f4e477499c9"},"schema_version":"1.0","source":{"id":"2101.08718","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.08718","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"arxiv_version","alias_value":"2101.08718v2","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.08718","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_12","alias_value":"TFXKNQSSND7A","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_16","alias_value":"TFXKNQSSND7ATURO","created_at":"2026-07-05T02:43:32Z"},{"alias_kind":"pith_short_8","alias_value":"TFXKNQSS","created_at":"2026-07-05T02:43:32Z"}],"graph_snapshots":[{"event_id":"sha256:add9d9efe5c1872350de511e5603d87d5beeb8cb00b1b000b5d9a18d7310dccc","target":"graph","created_at":"2026-07-05T02:43:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2101.08718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point $\\tau=i$, where modular invariant theories possess a residual $Z_4$ invariance. In this region the breaking of $Z_4$ can be fully described by the spurion $\\epsilon \\approx \\tau - i$, that flips its sign under $Z_4$. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the $Z_4$ symmetry at $\\tau=i$, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of $|\\epsilon|$. We present examples where","authors_text":"Andrea Romanino, Arsenii Titov, Ferruccio Feruglio, Valerio Gherardi","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2021-01-21T16:57:33Z","title":"Modular Invariant Dynamics and Fermion Mass Hierarchies around $\\tau = i$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.08718","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:f666a98d5b50393537e1f3729d9ec9a5b99082c4dac3e8c77eebc8613664d2c2","target":"record","created_at":"2026-07-05T02:43:32Z","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":"3d00fdbfa467c0c37f96ba5e473125b94ab67f855ba4ad71732ea5d54d82e568","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2021-01-21T16:57:33Z","title_canon_sha256":"da370f91d09b9e0375556b2b56c3a4a92d8c205528bab974364e8f4e477499c9"},"schema_version":"1.0","source":{"id":"2101.08718","kind":"arxiv","version":2}},"canonical_sha256":"996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85","first_computed_at":"2026-07-05T02:43:32.503261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:43:32.503261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JSjMwpIQWRo/Aw8sJnp4RfHO3b3KAbWAHeqcEI2loou98CI0bwyKKZB043F0wHF789QmTk77UsJnmKmmiNWKDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:43:32.504042Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.08718","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f666a98d5b50393537e1f3729d9ec9a5b99082c4dac3e8c77eebc8613664d2c2","sha256:add9d9efe5c1872350de511e5603d87d5beeb8cb00b1b000b5d9a18d7310dccc"],"state_sha256":"b60eae45b5dbd69618bc73d2b407aa5b3c4066f8cdcd177b260b04f428d63147"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/cGNXr33mCTnqV5JJEUXngN8cJmJQCk2EcVw1KzR7lP4LFKG8wDeTj0lHVpyxMZEpL5gUMlHLw28FUNmXzvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:01:10.787528Z","bundle_sha256":"b5079942a0f5e7aefe58cf49066ba69620a2d5691d4c39333b5f0918075b1534"}}