{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:B4HIZX72O6U7S5WGQT6TZW7C6T","short_pith_number":"pith:B4HIZX72","canonical_record":{"source":{"id":"1512.06950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T03:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"2bd2e43db02630517102bf0119dbc9d46bf9ab95028b53739cfeda6a36d54b42","abstract_canon_sha256":"a1dc9d44b70b610406875720516beca9141d38d4539f5534d31bf9f4346fdf6e"},"schema_version":"1.0"},"canonical_sha256":"0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417","source":{"kind":"arxiv","id":"1512.06950","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06950","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06950v2","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06950","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"B4HIZX72O6U7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B4HIZX72O6U7S5WG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B4HIZX72","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:B4HIZX72O6U7S5WGQT6TZW7C6T","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T03:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"2bd2e43db02630517102bf0119dbc9d46bf9ab95028b53739cfeda6a36d54b42","abstract_canon_sha256":"a1dc9d44b70b610406875720516beca9141d38d4539f5534d31bf9f4346fdf6e"},"schema_version":"1.0"},"canonical_sha256":"0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:57.676759Z","signature_b64":"hTgGbcgP1/cI5cpGlk0oe0QFaFEEek2WSVXp2SA1VEf00+7pYFW5fGbj/kEuIIVcIpfIfMz0/7R1JHoT7egrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417","last_reissued_at":"2026-05-18T01:04:57.676080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:57.676080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06950","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":"2026-05-18T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HtTU9Ke7oMByfZ7kqVk0G60RekyddTWjb5yrEHCEihE2133EtuMZDuGzzbdzOAsZMkCu8E/3WyeYhsudydBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:59:38.123400Z"},"content_sha256":"481beecf2c12a5edc7238600bdfcefa49b2de131722f43585eb361a243ea2308","schema_version":"1.0","event_id":"sha256:481beecf2c12a5edc7238600bdfcefa49b2de131722f43585eb361a243ea2308"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:B4HIZX72O6U7S5WGQT6TZW7C6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bose-Einstein condensation in a hyperbolic model for the Kompaneets equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gautam Iyer, Joshua Ballew, Robert L. Pego","submitted_at":"2015-12-22T03:48:51Z","abstract_excerpt":"In low-density or high-temperature plasmas, Compton scattering is the dominant process responsible for energy transport. Kompaneets in 1957 derived a non-linear degenerate parabolic equation for the photon energy distribution. In this paper we consider a simplified model obtained by neglecting diffusion of the photon number density in a particular way. We obtain a non-linear hyperbolic PDE with a position-dependent flux, which permits a one-parameter family of stationary entropy solutions to exist. We completely describe the long-time dynamics of each non-zero solution, showing that it approac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06950","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":"2026-05-18T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYEnwj2rYfsEKjqd1Gb7uQ8jNusTlAzqPjsenhK1NXLQVhQPxS7WFzEXUw/UT1oBIy93TSpS98HZypcQHtglBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:59:38.123754Z"},"content_sha256":"51bb982ab6ce503fbda8e46a9012d57a79292bf897bafa555f7f75f0090c1440","schema_version":"1.0","event_id":"sha256:51bb982ab6ce503fbda8e46a9012d57a79292bf897bafa555f7f75f0090c1440"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/bundle.json","state_url":"https://pith.science/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/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":"2026-06-23T08:59:38Z","links":{"resolver":"https://pith.science/pith/B4HIZX72O6U7S5WGQT6TZW7C6T","bundle":"https://pith.science/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/bundle.json","state":"https://pith.science/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4HIZX72O6U7S5WGQT6TZW7C6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B4HIZX72O6U7S5WGQT6TZW7C6T","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":"a1dc9d44b70b610406875720516beca9141d38d4539f5534d31bf9f4346fdf6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T03:48:51Z","title_canon_sha256":"2bd2e43db02630517102bf0119dbc9d46bf9ab95028b53739cfeda6a36d54b42"},"schema_version":"1.0","source":{"id":"1512.06950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06950","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06950v2","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06950","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"B4HIZX72O6U7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B4HIZX72O6U7S5WG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B4HIZX72","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:51bb982ab6ce503fbda8e46a9012d57a79292bf897bafa555f7f75f0090c1440","target":"graph","created_at":"2026-05-18T01:04:57Z","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":"In low-density or high-temperature plasmas, Compton scattering is the dominant process responsible for energy transport. Kompaneets in 1957 derived a non-linear degenerate parabolic equation for the photon energy distribution. In this paper we consider a simplified model obtained by neglecting diffusion of the photon number density in a particular way. We obtain a non-linear hyperbolic PDE with a position-dependent flux, which permits a one-parameter family of stationary entropy solutions to exist. We completely describe the long-time dynamics of each non-zero solution, showing that it approac","authors_text":"Gautam Iyer, Joshua Ballew, Robert L. Pego","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T03:48:51Z","title":"Bose-Einstein condensation in a hyperbolic model for the Kompaneets equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06950","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":"sha256:481beecf2c12a5edc7238600bdfcefa49b2de131722f43585eb361a243ea2308","target":"record","created_at":"2026-05-18T01:04:57Z","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":"a1dc9d44b70b610406875720516beca9141d38d4539f5534d31bf9f4346fdf6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T03:48:51Z","title_canon_sha256":"2bd2e43db02630517102bf0119dbc9d46bf9ab95028b53739cfeda6a36d54b42"},"schema_version":"1.0","source":{"id":"1512.06950","kind":"arxiv","version":2}},"canonical_sha256":"0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417","first_computed_at":"2026-05-18T01:04:57.676080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:57.676080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTgGbcgP1/cI5cpGlk0oe0QFaFEEek2WSVXp2SA1VEf00+7pYFW5fGbj/kEuIIVcIpfIfMz0/7R1JHoT7egrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:57.676759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:481beecf2c12a5edc7238600bdfcefa49b2de131722f43585eb361a243ea2308","sha256:51bb982ab6ce503fbda8e46a9012d57a79292bf897bafa555f7f75f0090c1440"],"state_sha256":"2b2096e1672f4fa6e7c23a87da9a044493db62ba57510858b76a885a9f505e3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M51LzAOvfkD3NSNuqHGdfC9UHo9z4SQJSjuOQsEV2s+V28w3WzQ6pGnM2M2MktJLB0Y52yPc23RoyVjGINh5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T08:59:38.125997Z","bundle_sha256":"f8cb510fa2e3b49970d4388b31b03901041dc3e63e6ac275c3bed00635a0d55b"}}