{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:GX6Y5DIQTQFBVDDNDPW7WX4MNG","short_pith_number":"pith:GX6Y5DIQ","canonical_record":{"source":{"id":"math/0211435","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2002-11-27T22:07:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a915ec904b4b43eb1b9210bdba37fbfffb382766ec184ce67f1c06cff99f8966","abstract_canon_sha256":"b2d3352ecea2ee82b9a5b165d1ee12d9247562deccf95c2986389e76621d8cc2"},"schema_version":"1.0"},"canonical_sha256":"35fd8e8d109c0a1a8c6d1bedfb5f8c6984457c1d5e81d2556aba605cece57c7a","source":{"kind":"arxiv","id":"math/0211435","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211435","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211435v2","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211435","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"GX6Y5DIQTQFB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"GX6Y5DIQTQFBVDDN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"GX6Y5DIQ","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:GX6Y5DIQTQFBVDDNDPW7WX4MNG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0211435","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2002-11-27T22:07:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a915ec904b4b43eb1b9210bdba37fbfffb382766ec184ce67f1c06cff99f8966","abstract_canon_sha256":"b2d3352ecea2ee82b9a5b165d1ee12d9247562deccf95c2986389e76621d8cc2"},"schema_version":"1.0"},"canonical_sha256":"35fd8e8d109c0a1a8c6d1bedfb5f8c6984457c1d5e81d2556aba605cece57c7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:28.586107Z","signature_b64":"5oxownTZCNY9U+2lxpdrjpATIGc1U3U6UeBPFZvgCzTLvbBu1V4VlCNN5tFFkjHFEZZwnkqECK2BCen2+G+vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35fd8e8d109c0a1a8c6d1bedfb5f8c6984457c1d5e81d2556aba605cece57c7a","last_reissued_at":"2026-05-18T04:28:28.585742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:28.585742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0211435","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFnlIaReavd9gDNOmYtyCu20/74JCFHJQFXHP5m8LPvGQ29Q3T06MDCIvyxach9kut8qrbhrpLzmZlvoKiUPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:32.699723Z"},"content_sha256":"7ed721a7fd4411695feb6c19c7fcb5b22c636dc0891a439bae8792653e9c7027","schema_version":"1.0","event_id":"sha256:7ed721a7fd4411695feb6c19c7fcb5b22c636dc0891a439bae8792653e9c7027"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:GX6Y5DIQTQFBVDDNDPW7WX4MNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Super-Brownian motion with extra birth at one point","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Carl Mueller, Klaus Fleischmann","submitted_at":"2002-11-27T22:07:15Z","abstract_excerpt":"A super-Brownian motion in two and three dimensions is constructed where \"particles\" give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based on Albeverio et al. (1995) who calculated the fundamental solutions of the heat equation with one-point potential in dimensions less than four."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211435","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sp6cJMVawtQ/sXrSVIDbq/LFNVPDF5fiTbfkbu/u39OVWEOSpKDFW2mmu/mrpNIx8kTtEgjel6F7Wv81GxaCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:32.700076Z"},"content_sha256":"cf9b5ffd07318aad8f9abc6b0da9f2fa5e6b41951938a34cf69ed5552a1b8146","schema_version":"1.0","event_id":"sha256:cf9b5ffd07318aad8f9abc6b0da9f2fa5e6b41951938a34cf69ed5552a1b8146"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/bundle.json","state_url":"https://pith.science/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/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":"2026-06-02T03:54:32Z","links":{"resolver":"https://pith.science/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG","bundle":"https://pith.science/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/bundle.json","state":"https://pith.science/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GX6Y5DIQTQFBVDDNDPW7WX4MNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:GX6Y5DIQTQFBVDDNDPW7WX4MNG","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":"b2d3352ecea2ee82b9a5b165d1ee12d9247562deccf95c2986389e76621d8cc2","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2002-11-27T22:07:15Z","title_canon_sha256":"a915ec904b4b43eb1b9210bdba37fbfffb382766ec184ce67f1c06cff99f8966"},"schema_version":"1.0","source":{"id":"math/0211435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211435","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211435v2","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211435","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"GX6Y5DIQTQFB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"GX6Y5DIQTQFBVDDN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"GX6Y5DIQ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:cf9b5ffd07318aad8f9abc6b0da9f2fa5e6b41951938a34cf69ed5552a1b8146","target":"graph","created_at":"2026-05-18T04:28:28Z","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":"A super-Brownian motion in two and three dimensions is constructed where \"particles\" give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based on Albeverio et al. (1995) who calculated the fundamental solutions of the heat equation with one-point potential in dimensions less than four.","authors_text":"Carl Mueller, Klaus Fleischmann","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2002-11-27T22:07:15Z","title":"Super-Brownian motion with extra birth at one point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211435","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":"sha256:7ed721a7fd4411695feb6c19c7fcb5b22c636dc0891a439bae8792653e9c7027","target":"record","created_at":"2026-05-18T04:28:28Z","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":"b2d3352ecea2ee82b9a5b165d1ee12d9247562deccf95c2986389e76621d8cc2","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2002-11-27T22:07:15Z","title_canon_sha256":"a915ec904b4b43eb1b9210bdba37fbfffb382766ec184ce67f1c06cff99f8966"},"schema_version":"1.0","source":{"id":"math/0211435","kind":"arxiv","version":2}},"canonical_sha256":"35fd8e8d109c0a1a8c6d1bedfb5f8c6984457c1d5e81d2556aba605cece57c7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35fd8e8d109c0a1a8c6d1bedfb5f8c6984457c1d5e81d2556aba605cece57c7a","first_computed_at":"2026-05-18T04:28:28.585742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.585742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5oxownTZCNY9U+2lxpdrjpATIGc1U3U6UeBPFZvgCzTLvbBu1V4VlCNN5tFFkjHFEZZwnkqECK2BCen2+G+vAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.586107Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ed721a7fd4411695feb6c19c7fcb5b22c636dc0891a439bae8792653e9c7027","sha256:cf9b5ffd07318aad8f9abc6b0da9f2fa5e6b41951938a34cf69ed5552a1b8146"],"state_sha256":"0ff65bede1b5584e6261582527736592846ca20d88f23b2ad044ebc7437844a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAtfaCt2xQBTjtiKmTebwrhs/yE6KxVgqMBCT8pYNhr5EmR3m6u/CUHDbRwo83ADQ+BMdpat95bsrO2cFjY4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:54:32.702042Z","bundle_sha256":"e0c693c34a7576f8b8d8d72bec9eda1d203ba3966944d45b4d8866f0ff2a744e"}}