{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:U7BWV2JEABQZ6OVJVZU4Z454CH","short_pith_number":"pith:U7BWV2JE","canonical_record":{"source":{"id":"math-ph/0612003","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-12-01T09:16:19Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"d4b25dede0da99a637830c118912504ac15e27e70eddbe7214282e02b434030b","abstract_canon_sha256":"db9640c583f0d5c76b83bf73f567fbd2c1d48da2bf3d69e9ec6186767d7b7df8"},"schema_version":"1.0"},"canonical_sha256":"a7c36ae92400619f3aa9ae69ccf3bc11f0ad68a56873730f82e3b157fabdfbce","source":{"kind":"arxiv","id":"math-ph/0612003","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0612003","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0612003v3","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0612003","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"U7BWV2JEABQZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"U7BWV2JEABQZ6OVJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"U7BWV2JE","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:U7BWV2JEABQZ6OVJVZU4Z454CH","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0612003","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-12-01T09:16:19Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"d4b25dede0da99a637830c118912504ac15e27e70eddbe7214282e02b434030b","abstract_canon_sha256":"db9640c583f0d5c76b83bf73f567fbd2c1d48da2bf3d69e9ec6186767d7b7df8"},"schema_version":"1.0"},"canonical_sha256":"a7c36ae92400619f3aa9ae69ccf3bc11f0ad68a56873730f82e3b157fabdfbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:38.661628Z","signature_b64":"nWHxJ4diP8HBEIcB4z/dTxKdsGWqEjIXlxaVwkqpaOiI91qI9cd6kUmg8fBU9VfjPv18a9ppBlWJbjBRhtk0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c36ae92400619f3aa9ae69ccf3bc11f0ad68a56873730f82e3b157fabdfbce","last_reissued_at":"2026-05-18T02:35:38.661142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:38.661142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0612003","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJLeuBYrTYLiYRn69qbq63qpxLz6nRN3S1wkWdLesK1K3lpvbQkcCeupeu4O3AZ2CPQiNo/lb9lfXDNt3fVVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:15:14.442460Z"},"content_sha256":"439d74b4d80df459cc560570b98f7670c95c22867c3b4b8dd749e4fa9f67653c","schema_version":"1.0","event_id":"sha256:439d74b4d80df459cc560570b98f7670c95c22867c3b4b8dd749e4fa9f67653c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:U7BWV2JEABQZ6OVJVZU4Z454CH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Regularized Fermionic Projector of the Vacuum","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Felix Finster","submitted_at":"2006-12-01T09:16:19Z","abstract_excerpt":"We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional ${\\mathcal{M}} P$-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0612003","kind":"arxiv","version":3},"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":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7ZxHJnei43he+5/GSna1lw74TTLQR2nrNsYf2Meqe2/4TdSvQyJMajjt/QawPZaF5xlhJgaOjAygYuWIpQuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:15:14.442808Z"},"content_sha256":"d452103c0247dde1899fd2371262926378dde576458a666c5ff220c0303e8bc0","schema_version":"1.0","event_id":"sha256:d452103c0247dde1899fd2371262926378dde576458a666c5ff220c0303e8bc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/bundle.json","state_url":"https://pith.science/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/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":"2026-06-01T18:15:14Z","links":{"resolver":"https://pith.science/pith/U7BWV2JEABQZ6OVJVZU4Z454CH","bundle":"https://pith.science/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/bundle.json","state":"https://pith.science/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7BWV2JEABQZ6OVJVZU4Z454CH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:U7BWV2JEABQZ6OVJVZU4Z454CH","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":"db9640c583f0d5c76b83bf73f567fbd2c1d48da2bf3d69e9ec6186767d7b7df8","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-12-01T09:16:19Z","title_canon_sha256":"d4b25dede0da99a637830c118912504ac15e27e70eddbe7214282e02b434030b"},"schema_version":"1.0","source":{"id":"math-ph/0612003","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0612003","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0612003v3","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0612003","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"U7BWV2JEABQZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"U7BWV2JEABQZ6OVJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"U7BWV2JE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:d452103c0247dde1899fd2371262926378dde576458a666c5ff220c0303e8bc0","target":"graph","created_at":"2026-05-18T02:35:38Z","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 construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional ${\\mathcal{M}} P$-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.","authors_text":"Felix Finster","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-12-01T09:16:19Z","title":"On the Regularized Fermionic Projector of the Vacuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0612003","kind":"arxiv","version":3},"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":"sha256:439d74b4d80df459cc560570b98f7670c95c22867c3b4b8dd749e4fa9f67653c","target":"record","created_at":"2026-05-18T02:35:38Z","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":"db9640c583f0d5c76b83bf73f567fbd2c1d48da2bf3d69e9ec6186767d7b7df8","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-12-01T09:16:19Z","title_canon_sha256":"d4b25dede0da99a637830c118912504ac15e27e70eddbe7214282e02b434030b"},"schema_version":"1.0","source":{"id":"math-ph/0612003","kind":"arxiv","version":3}},"canonical_sha256":"a7c36ae92400619f3aa9ae69ccf3bc11f0ad68a56873730f82e3b157fabdfbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c36ae92400619f3aa9ae69ccf3bc11f0ad68a56873730f82e3b157fabdfbce","first_computed_at":"2026-05-18T02:35:38.661142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.661142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nWHxJ4diP8HBEIcB4z/dTxKdsGWqEjIXlxaVwkqpaOiI91qI9cd6kUmg8fBU9VfjPv18a9ppBlWJbjBRhtk0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.661628Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0612003","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:439d74b4d80df459cc560570b98f7670c95c22867c3b4b8dd749e4fa9f67653c","sha256:d452103c0247dde1899fd2371262926378dde576458a666c5ff220c0303e8bc0"],"state_sha256":"c1a2f5241c6167f7d2fae2444b068d4b42975140178b27e8ec118240e77f0c30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPfTv1pejjOZCD12QhWm3SvW96+PCepus1eMELu9tbJ7DaR8UO8tp45Rd3mSyK5BvvQ5xl/+MTFtnhTLAzf7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:15:14.444825Z","bundle_sha256":"26e36ddf78884251022aadeb150d31329478b66d39e1e92a4b8ff2526d175bac"}}