{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5ECJFFYAGSM5E6THXBXY5V564V","short_pith_number":"pith:5ECJFFYA","canonical_record":{"source":{"id":"1612.06916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-20T23:16:39Z","cross_cats_sorted":[],"title_canon_sha256":"10ab2e69a20af6d3fd76a5f000ff9fee6a9f4f21f2d00e0af4dfa24ae7ad2e84","abstract_canon_sha256":"49c0046fc496a9fe1deaed5c1e774690e2225db20c91a2c34a6bb555415f01e3"},"schema_version":"1.0"},"canonical_sha256":"e9049297003499d27a67b86f8ed7bee54013c0e8e45d5e7445432d0cda368428","source":{"kind":"arxiv","id":"1612.06916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06916","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06916v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06916","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"5ECJFFYAGSM5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5ECJFFYAGSM5E6TH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5ECJFFYA","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5ECJFFYAGSM5E6THXBXY5V564V","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-20T23:16:39Z","cross_cats_sorted":[],"title_canon_sha256":"10ab2e69a20af6d3fd76a5f000ff9fee6a9f4f21f2d00e0af4dfa24ae7ad2e84","abstract_canon_sha256":"49c0046fc496a9fe1deaed5c1e774690e2225db20c91a2c34a6bb555415f01e3"},"schema_version":"1.0"},"canonical_sha256":"e9049297003499d27a67b86f8ed7bee54013c0e8e45d5e7445432d0cda368428","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:15.064335Z","signature_b64":"2kvGrQow93wTjfBrUqQp0c397OLdsV9SXNgZyAB3+yGNyxDwGQ2IIA0KD/FJfZ0bHayPH/AYiRwIi7x7LRNRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9049297003499d27a67b86f8ed7bee54013c0e8e45d5e7445432d0cda368428","last_reissued_at":"2026-05-18T00:54:15.063807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:15.063807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06916","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEHDqLb1wZWI7hWf6abux/R4VnMay/ieLcE7jt0j7QXILto7jMtem9hdfaDDylOM5s51oeC+eGvXn8DylcbYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:42:00.300987Z"},"content_sha256":"fe9f0c6f34c3e26803a6f271ff7d8d301470684b628023589f97450f16e4ec3d","schema_version":"1.0","event_id":"sha256:fe9f0c6f34c3e26803a6f271ff7d8d301470684b628023589f97450f16e4ec3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5ECJFFYAGSM5E6THXBXY5V564V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L infinity resolvent bounds for steady Boltzmann's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kevin Zumbrun","submitted_at":"2016-12-20T23:16:39Z","abstract_excerpt":"We derive lower bounds on the resolvent operator for the linearized steady Boltzmann equation over weighted L1 Banach spaces in velocity, comparable to those derived by Pogan & Zumbrun in an analogous weighted L2 Hilbert space setting. These show in particular that the operator norm of the resolvent kernel is unbounded in Lp(R) for all $1<p \\leq \\infty$, resolving an apparent discrepancy in behavior between the two settings suggested by previous work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06916","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U4MfxkNN2Ggx3CHYWDZpWG/hFfFzTqEVFsj5FOZJyWZsdSS7DTcIwreBGj527bz/5eh+dnc3Im9KZS2ggBjfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:42:00.301593Z"},"content_sha256":"809e44fbf035748f985539a536e65c74869d5977404259a67aafc9d4cf27b37f","schema_version":"1.0","event_id":"sha256:809e44fbf035748f985539a536e65c74869d5977404259a67aafc9d4cf27b37f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ECJFFYAGSM5E6THXBXY5V564V/bundle.json","state_url":"https://pith.science/pith/5ECJFFYAGSM5E6THXBXY5V564V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ECJFFYAGSM5E6THXBXY5V564V/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":"2026-05-28T05:42:00Z","links":{"resolver":"https://pith.science/pith/5ECJFFYAGSM5E6THXBXY5V564V","bundle":"https://pith.science/pith/5ECJFFYAGSM5E6THXBXY5V564V/bundle.json","state":"https://pith.science/pith/5ECJFFYAGSM5E6THXBXY5V564V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ECJFFYAGSM5E6THXBXY5V564V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5ECJFFYAGSM5E6THXBXY5V564V","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":"49c0046fc496a9fe1deaed5c1e774690e2225db20c91a2c34a6bb555415f01e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-20T23:16:39Z","title_canon_sha256":"10ab2e69a20af6d3fd76a5f000ff9fee6a9f4f21f2d00e0af4dfa24ae7ad2e84"},"schema_version":"1.0","source":{"id":"1612.06916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06916","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06916v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06916","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"5ECJFFYAGSM5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5ECJFFYAGSM5E6TH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5ECJFFYA","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:809e44fbf035748f985539a536e65c74869d5977404259a67aafc9d4cf27b37f","target":"graph","created_at":"2026-05-18T00:54:15Z","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 derive lower bounds on the resolvent operator for the linearized steady Boltzmann equation over weighted L1 Banach spaces in velocity, comparable to those derived by Pogan & Zumbrun in an analogous weighted L2 Hilbert space setting. These show in particular that the operator norm of the resolvent kernel is unbounded in Lp(R) for all $1<p \\leq \\infty$, resolving an apparent discrepancy in behavior between the two settings suggested by previous work.","authors_text":"Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-20T23:16:39Z","title":"L infinity resolvent bounds for steady Boltzmann's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06916","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:fe9f0c6f34c3e26803a6f271ff7d8d301470684b628023589f97450f16e4ec3d","target":"record","created_at":"2026-05-18T00:54:15Z","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":"49c0046fc496a9fe1deaed5c1e774690e2225db20c91a2c34a6bb555415f01e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-20T23:16:39Z","title_canon_sha256":"10ab2e69a20af6d3fd76a5f000ff9fee6a9f4f21f2d00e0af4dfa24ae7ad2e84"},"schema_version":"1.0","source":{"id":"1612.06916","kind":"arxiv","version":1}},"canonical_sha256":"e9049297003499d27a67b86f8ed7bee54013c0e8e45d5e7445432d0cda368428","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9049297003499d27a67b86f8ed7bee54013c0e8e45d5e7445432d0cda368428","first_computed_at":"2026-05-18T00:54:15.063807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.063807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2kvGrQow93wTjfBrUqQp0c397OLdsV9SXNgZyAB3+yGNyxDwGQ2IIA0KD/FJfZ0bHayPH/AYiRwIi7x7LRNRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.064335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe9f0c6f34c3e26803a6f271ff7d8d301470684b628023589f97450f16e4ec3d","sha256:809e44fbf035748f985539a536e65c74869d5977404259a67aafc9d4cf27b37f"],"state_sha256":"b7209e06e0e85e9761be13e5e5789b776858e493ef711b833e413f5fdaf1d495"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9aGxlKTbbRupPttZcaBg99/5RfIqmK4DznSKt5AyJeTgDTLQmGsaZswIRp3ZBm2AFijyfGBnUgkkImpadfTdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:42:00.304942Z","bundle_sha256":"559d3604ff146d422d0d862fa3804fbaff02108a0ffd62ce2592d3ef3b8c6275"}}