{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:2XJV77TIJMQ3IXGPU3PSUO3ZSR","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":"e4b3603e26a55e89d59edcc34993c0292757947c4e76aea17ae3748b02f595e5","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"hep-ph","submitted_at":"2000-07-28T20:16:17Z","title_canon_sha256":"e56e2bf61355ef0ce0ec181a0a0fe956a31eef76a38cab84d6aba0d859fe562f"},"schema_version":"1.0","source":{"id":"hep-ph/0007343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0007343","created_at":"2026-07-04T16:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0007343v2","created_at":"2026-07-04T16:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0007343","created_at":"2026-07-04T16:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"2XJV77TIJMQ3","created_at":"2026-07-04T16:20:16Z"},{"alias_kind":"pith_short_16","alias_value":"2XJV77TIJMQ3IXGP","created_at":"2026-07-04T16:20:16Z"},{"alias_kind":"pith_short_8","alias_value":"2XJV77TI","created_at":"2026-07-04T16:20:16Z"}],"graph_snapshots":[{"event_id":"sha256:e4fc8437f54abfecf2f60fbb3dc4d48735fa8673cc55e56510e5c52f5abca1c6","target":"graph","created_at":"2026-07-04T16:20:16Z","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/hep-ph/0007343/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the a","authors_text":"Dejan Stojkovic","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2000-07-28T20:16:17Z","title":"Fermionic Zero Modes on Domain Walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0007343","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":"sha256:2e24a77dd2070d620a97a3e4dfb2596dc9a8ba5142a6c88e9f587f3a22684e35","target":"record","created_at":"2026-07-04T16:20:16Z","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":"e4b3603e26a55e89d59edcc34993c0292757947c4e76aea17ae3748b02f595e5","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"hep-ph","submitted_at":"2000-07-28T20:16:17Z","title_canon_sha256":"e56e2bf61355ef0ce0ec181a0a0fe956a31eef76a38cab84d6aba0d859fe562f"},"schema_version":"1.0","source":{"id":"hep-ph/0007343","kind":"arxiv","version":2}},"canonical_sha256":"d5d35ffe684b21b45ccfa6df2a3b799446e2d360889d1290f9f2f7a7927ae5cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5d35ffe684b21b45ccfa6df2a3b799446e2d360889d1290f9f2f7a7927ae5cc","first_computed_at":"2026-07-04T16:20:16.366890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:20:16.366890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hwLAuZd5LQXODuSFo3QqR9CfKcdy5cOe88BZimHs7Ws5wAnOrpkPedRTgxnooMIhyDiv73zbR7Ojud8odhfcCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:20:16.367309Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0007343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e24a77dd2070d620a97a3e4dfb2596dc9a8ba5142a6c88e9f587f3a22684e35","sha256:e4fc8437f54abfecf2f60fbb3dc4d48735fa8673cc55e56510e5c52f5abca1c6"],"state_sha256":"4a9731bbff8aedbdd2a4a7f33765d1c1400b7df25934f21ac3813a636e34c1bf"}