{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HVNPWF7BVFHY4TZ2V2K7VRRXL6","short_pith_number":"pith:HVNPWF7B","canonical_record":{"source":{"id":"1804.06192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T12:20:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7fd96c8decca52bcbded8d3076046e9543abc7d15dad06b2d8f6e9f99ed77b89","abstract_canon_sha256":"c1d6ff3875368e1c062d3dc7425b00681f21c68dd7633eb6a8d890fd92980a0f"},"schema_version":"1.0"},"canonical_sha256":"3d5afb17e1a94f8e4f3aae95fac6375f8617071ca417f72c2813e8da737ab4d6","source":{"kind":"arxiv","id":"1804.06192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06192","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06192v2","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06192","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"HVNPWF7BVFHY","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HVNPWF7BVFHY4TZ2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HVNPWF7B","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HVNPWF7BVFHY4TZ2V2K7VRRXL6","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T12:20:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7fd96c8decca52bcbded8d3076046e9543abc7d15dad06b2d8f6e9f99ed77b89","abstract_canon_sha256":"c1d6ff3875368e1c062d3dc7425b00681f21c68dd7633eb6a8d890fd92980a0f"},"schema_version":"1.0"},"canonical_sha256":"3d5afb17e1a94f8e4f3aae95fac6375f8617071ca417f72c2813e8da737ab4d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:59.349404Z","signature_b64":"O4GI+1+xLWDQVSjXDRvVT4Zy+GuKc5FnWS5kf47U4gaXb4n8z0wEENRaHpgVI9YvNtn8fCA9jSzh47x83Qa+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d5afb17e1a94f8e4f3aae95fac6375f8617071ca417f72c2813e8da737ab4d6","last_reissued_at":"2026-05-18T00:17:59.348739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:59.348739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06192","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":"2026-05-18T00:17:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lGAGecxlvDsN6yPwKQKkk5FFIdCyg6bmZsDkYuwjLPfmAazdrvoW9YSpfBGhcI7RreTWtR6d3MDFwwr+YAjTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:19:07.985820Z"},"content_sha256":"0fbb8f85132e92bd16c1f98c7ef57871ef3558b5a88adeeb2d54f5db53ca27bd","schema_version":"1.0","event_id":"sha256:0fbb8f85132e92bd16c1f98c7ef57871ef3558b5a88adeeb2d54f5db53ca27bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HVNPWF7BVFHY4TZ2V2K7VRRXL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence to self-similarity for ballistic annihilation dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Ricardo Alonso (PUC-RIO), V Eronique Bagland, V\\'eronique Bagland (LMBP)","submitted_at":"2018-04-17T12:20:57Z","abstract_excerpt":"We consider the spatially homogeneous Boltzmann equation for ballistic annihilation in dimension d 2. Such model describes a system of ballistic hard spheres that, at the moment of interaction, either annihilate with probability $\\alpha$ $\\in$ (0, 1) or collide elastically with probability 1 -- $\\alpha$. Such equation is highly dissipative in the sense that all observables, hence solutions, vanish as time progresses. Following a contribution , by two of the authors, considering well posedness of the steady self-similar profile in the regime of small annihilation rate $\\alpha$ $\\ll$ 1, we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06192","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":"2026-05-18T00:17:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+m3lG4DgY5nzAePkzGWkt9zAIFat2NCIcZJIVQLVl7vq8rh1bWsAPPlRZGzk/UV0qSQ6eDPQfZbyQgPRWvx6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:19:07.986159Z"},"content_sha256":"9049d4a19727bf88c9719fafb7adb58d24d4cf4a511f13b28d2b06760943a050","schema_version":"1.0","event_id":"sha256:9049d4a19727bf88c9719fafb7adb58d24d4cf4a511f13b28d2b06760943a050"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/bundle.json","state_url":"https://pith.science/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/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":"2026-06-20T14:19:07Z","links":{"resolver":"https://pith.science/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6","bundle":"https://pith.science/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/bundle.json","state":"https://pith.science/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVNPWF7BVFHY4TZ2V2K7VRRXL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HVNPWF7BVFHY4TZ2V2K7VRRXL6","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":"c1d6ff3875368e1c062d3dc7425b00681f21c68dd7633eb6a8d890fd92980a0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T12:20:57Z","title_canon_sha256":"7fd96c8decca52bcbded8d3076046e9543abc7d15dad06b2d8f6e9f99ed77b89"},"schema_version":"1.0","source":{"id":"1804.06192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06192","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06192v2","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06192","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"HVNPWF7BVFHY","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HVNPWF7BVFHY4TZ2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HVNPWF7B","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:9049d4a19727bf88c9719fafb7adb58d24d4cf4a511f13b28d2b06760943a050","target":"graph","created_at":"2026-05-18T00:17:59Z","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 consider the spatially homogeneous Boltzmann equation for ballistic annihilation in dimension d 2. Such model describes a system of ballistic hard spheres that, at the moment of interaction, either annihilate with probability $\\alpha$ $\\in$ (0, 1) or collide elastically with probability 1 -- $\\alpha$. Such equation is highly dissipative in the sense that all observables, hence solutions, vanish as time progresses. Following a contribution , by two of the authors, considering well posedness of the steady self-similar profile in the regime of small annihilation rate $\\alpha$ $\\ll$ 1, we prove","authors_text":"Bertrand Lods, Ricardo Alonso (PUC-RIO), V Eronique Bagland, V\\'eronique Bagland (LMBP)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T12:20:57Z","title":"Convergence to self-similarity for ballistic annihilation dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06192","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":"sha256:0fbb8f85132e92bd16c1f98c7ef57871ef3558b5a88adeeb2d54f5db53ca27bd","target":"record","created_at":"2026-05-18T00:17:59Z","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":"c1d6ff3875368e1c062d3dc7425b00681f21c68dd7633eb6a8d890fd92980a0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T12:20:57Z","title_canon_sha256":"7fd96c8decca52bcbded8d3076046e9543abc7d15dad06b2d8f6e9f99ed77b89"},"schema_version":"1.0","source":{"id":"1804.06192","kind":"arxiv","version":2}},"canonical_sha256":"3d5afb17e1a94f8e4f3aae95fac6375f8617071ca417f72c2813e8da737ab4d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d5afb17e1a94f8e4f3aae95fac6375f8617071ca417f72c2813e8da737ab4d6","first_computed_at":"2026-05-18T00:17:59.348739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:59.348739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O4GI+1+xLWDQVSjXDRvVT4Zy+GuKc5FnWS5kf47U4gaXb4n8z0wEENRaHpgVI9YvNtn8fCA9jSzh47x83Qa+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:59.349404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fbb8f85132e92bd16c1f98c7ef57871ef3558b5a88adeeb2d54f5db53ca27bd","sha256:9049d4a19727bf88c9719fafb7adb58d24d4cf4a511f13b28d2b06760943a050"],"state_sha256":"39b40ff8f94b4d7ed40a2526827237c139e6278a94940af6bf577a99e3eb2824"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tQxB3BUtzN5MHs6d8ZuHUG4ek9mYDal7vGUjpib0QkQxV6UNCO/7H50UHEaveMpKMZzIXQvISmdycTSb6ytSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:19:07.988003Z","bundle_sha256":"3d7cbbe178ea887c98912fc501a87996f7f285bbfbb9758ca9fc743ea4a80cb8"}}