{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:T7I5MGUN7EREABREORVPQ72IJX","short_pith_number":"pith:T7I5MGUN","canonical_record":{"source":{"id":"math/0611727","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-11-23T14:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"ec6e479aa9be8aa8b906a029f54a61c33a5960d5a9af2de42853df67d10ce398","abstract_canon_sha256":"2a76870cc6e7782466031466438428b9ecb45bc2b759ae8983fa44d8c122f975"},"schema_version":"1.0"},"canonical_sha256":"9fd1d61a8df922400624746af87f484dfecf4e5b28e75f66603ffd96bf2e8084","source":{"kind":"arxiv","id":"math/0611727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611727","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611727v1","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611727","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"T7I5MGUN7ERE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"T7I5MGUN7EREABRE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"T7I5MGUN","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:T7I5MGUN7EREABREORVPQ72IJX","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611727","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-11-23T14:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"ec6e479aa9be8aa8b906a029f54a61c33a5960d5a9af2de42853df67d10ce398","abstract_canon_sha256":"2a76870cc6e7782466031466438428b9ecb45bc2b759ae8983fa44d8c122f975"},"schema_version":"1.0"},"canonical_sha256":"9fd1d61a8df922400624746af87f484dfecf4e5b28e75f66603ffd96bf2e8084","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.543151Z","signature_b64":"e3mGywqhJbclJ2EMTTlnLzeJ37JINafsAq7SSqPh50TnAF7glupOUZ2hWoGc4RkZX+xAJcy/PGYcaY+3QQ6tBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fd1d61a8df922400624746af87f484dfecf4e5b28e75f66603ffd96bf2e8084","last_reissued_at":"2026-05-18T01:38:23.542502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.542502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611727","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":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+dN8y3FICmN96aKg83bO+Nj8y7aI6kKvylpTX4eXRtB7Q1irCRD+iaCC5HtOirT8XmrlyPrgmzMBvPdz7AYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:36:16.075066Z"},"content_sha256":"fca63d9992f38f5169918dbbeb9076c44147427c50812e93a9e8e3fc22caa745","schema_version":"1.0","event_id":"sha256:fca63d9992f38f5169918dbbeb9076c44147427c50812e93a9e8e3fc22caa745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:T7I5MGUN7EREABREORVPQ72IJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Intersection Local Time of $(\\alpha,d,\\beta)$-superprocess","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. Villa, L. Mytnik","submitted_at":"2006-11-23T14:48:48Z","abstract_excerpt":"The existence of self-intersection local time (SILT), when the time diagonal is intersected, of the $(\\alpha,d,\\beta)$-superprocess is proved for $d/2<\\alpha $ and for a renormalized SILT when $d/(2+(1+\\beta)^{-1})<\\alpha \\leq d/2$. We also establish Tanaka-like formula for SILT."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611727","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":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EEgE3mILsWt5gemT52POjzLuOUFvGq9aNcjHPESApla2ndcvpnV+oDjK04scIITGaOUDXqlVulfWQhCDSjaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:36:16.075445Z"},"content_sha256":"1522f028959fc09964779d7c5fc5c7659a5ecde1c74a8fc1e9fbf940f2b16c50","schema_version":"1.0","event_id":"sha256:1522f028959fc09964779d7c5fc5c7659a5ecde1c74a8fc1e9fbf940f2b16c50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7I5MGUN7EREABREORVPQ72IJX/bundle.json","state_url":"https://pith.science/pith/T7I5MGUN7EREABREORVPQ72IJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7I5MGUN7EREABREORVPQ72IJX/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":"2026-06-12T09:36:16Z","links":{"resolver":"https://pith.science/pith/T7I5MGUN7EREABREORVPQ72IJX","bundle":"https://pith.science/pith/T7I5MGUN7EREABREORVPQ72IJX/bundle.json","state":"https://pith.science/pith/T7I5MGUN7EREABREORVPQ72IJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7I5MGUN7EREABREORVPQ72IJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:T7I5MGUN7EREABREORVPQ72IJX","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":"2a76870cc6e7782466031466438428b9ecb45bc2b759ae8983fa44d8c122f975","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-11-23T14:48:48Z","title_canon_sha256":"ec6e479aa9be8aa8b906a029f54a61c33a5960d5a9af2de42853df67d10ce398"},"schema_version":"1.0","source":{"id":"math/0611727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611727","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611727v1","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611727","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"T7I5MGUN7ERE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"T7I5MGUN7EREABRE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"T7I5MGUN","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:1522f028959fc09964779d7c5fc5c7659a5ecde1c74a8fc1e9fbf940f2b16c50","target":"graph","created_at":"2026-05-18T01:38:23Z","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":"The existence of self-intersection local time (SILT), when the time diagonal is intersected, of the $(\\alpha,d,\\beta)$-superprocess is proved for $d/2<\\alpha $ and for a renormalized SILT when $d/(2+(1+\\beta)^{-1})<\\alpha \\leq d/2$. We also establish Tanaka-like formula for SILT.","authors_text":"J. Villa, L. Mytnik","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-11-23T14:48:48Z","title":"Self-Intersection Local Time of $(\\alpha,d,\\beta)$-superprocess"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611727","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:fca63d9992f38f5169918dbbeb9076c44147427c50812e93a9e8e3fc22caa745","target":"record","created_at":"2026-05-18T01:38:23Z","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":"2a76870cc6e7782466031466438428b9ecb45bc2b759ae8983fa44d8c122f975","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-11-23T14:48:48Z","title_canon_sha256":"ec6e479aa9be8aa8b906a029f54a61c33a5960d5a9af2de42853df67d10ce398"},"schema_version":"1.0","source":{"id":"math/0611727","kind":"arxiv","version":1}},"canonical_sha256":"9fd1d61a8df922400624746af87f484dfecf4e5b28e75f66603ffd96bf2e8084","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fd1d61a8df922400624746af87f484dfecf4e5b28e75f66603ffd96bf2e8084","first_computed_at":"2026-05-18T01:38:23.542502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:23.542502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e3mGywqhJbclJ2EMTTlnLzeJ37JINafsAq7SSqPh50TnAF7glupOUZ2hWoGc4RkZX+xAJcy/PGYcaY+3QQ6tBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:23.543151Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fca63d9992f38f5169918dbbeb9076c44147427c50812e93a9e8e3fc22caa745","sha256:1522f028959fc09964779d7c5fc5c7659a5ecde1c74a8fc1e9fbf940f2b16c50"],"state_sha256":"a90e71419274001a6d36d6061ccb422a29caaaadd0ae9e5acb2af48ce365e1b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gcMOEPGKqYNCarRV+Qg9t8qFaCESU3tRWHnx8jHshT5JmNUk37xAfuEr594ndiFBEdGa8c+9oDzOCZy+kFmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:36:16.077464Z","bundle_sha256":"f379e9cab0a9e137a9f7aee3d272499cd0722f448ed9fdf1a28f4434e989bb03"}}