{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HA2XLYDTT66YMILWAR2ETXOZNW","short_pith_number":"pith:HA2XLYDT","canonical_record":{"source":{"id":"2303.11289","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-20T17:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"a6c42b2c52a56fe0add67f41d0a0903ec17db8f7aea6568489eba8a52ea7edff","abstract_canon_sha256":"4557ee4372a874cdbd7fd784fc1bd90e9e415f0f9040130debb52adbd023ee80"},"schema_version":"1.0"},"canonical_sha256":"383575e0739fbd862176047449ddd96d8d3de34b9c694fb9c8cc02631c8b644a","source":{"kind":"arxiv","id":"2303.11289","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.11289","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"2303.11289v3","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.11289","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"HA2XLYDTT66Y","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_16","alias_value":"HA2XLYDTT66YMILW","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_8","alias_value":"HA2XLYDT","created_at":"2026-07-05T10:38:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HA2XLYDTT66YMILWAR2ETXOZNW","target":"record","payload":{"canonical_record":{"source":{"id":"2303.11289","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-20T17:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"a6c42b2c52a56fe0add67f41d0a0903ec17db8f7aea6568489eba8a52ea7edff","abstract_canon_sha256":"4557ee4372a874cdbd7fd784fc1bd90e9e415f0f9040130debb52adbd023ee80"},"schema_version":"1.0"},"canonical_sha256":"383575e0739fbd862176047449ddd96d8d3de34b9c694fb9c8cc02631c8b644a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:38:19.342192Z","signature_b64":"dF1m+VkJOLznTk/ea04Cmd9mO9gG2vUlJTfMrQ3CR9axniDU9h0I1AKbTZDGECboN22XU4UZNd1ZZNANCWfmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"383575e0739fbd862176047449ddd96d8d3de34b9c694fb9c8cc02631c8b644a","last_reissued_at":"2026-07-05T10:38:19.341694Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:38:19.341694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.11289","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2evXf4lFuwloCskDNwJJdUla1gX1V1lrJn/K3XRkAPJt20YckQA6jnGUCvRCKXGzaV57w2y+aiHaDtcHN0FnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:08:22.337514Z"},"content_sha256":"1830ba9654a7dc8e571bf28cb6f419377298261b1fd326cce40ecaf3789d7e7b","schema_version":"1.0","event_id":"sha256:1830ba9654a7dc8e571bf28cb6f419377298261b1fd326cce40ecaf3789d7e7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HA2XLYDTT66YMILWAR2ETXOZNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Porous Medium Equation: Large Deviations and Gradient Flow with Degenerate and Unbounded Diffusion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin Gess, Daniel Heydecker","submitted_at":"2023-03-20T17:26:08Z","abstract_excerpt":"The problem of deriving a gradient flow structure for the porous medium equation which is {\\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range process with jump rate $g(k)=k^\\alpha, \\alpha>1$ is considered, and its hydrodynamic limit and dynamical large deviations are shown in the presence of both degenerate and unbounded diffusion. The key superexponential estimate is obtained using pathwise discretised regularity estimates in the spirit of the Aubin-Lions-Simons lemma. This allows to exhibit the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.11289","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.11289/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oC9BmuZ7PUe1F3eXvVDqcX9x5d4xYuDZHzW8iJgvUpWQBpvxkDON0sG7b+WzAv1hrWkGicUVdmfKjJocTn1oAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:08:22.338090Z"},"content_sha256":"7c54efdbc2850c95f591c5953b56bed529b126ecd0f7de1dad4718cdbb45f80f","schema_version":"1.0","event_id":"sha256:7c54efdbc2850c95f591c5953b56bed529b126ecd0f7de1dad4718cdbb45f80f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HA2XLYDTT66YMILWAR2ETXOZNW/bundle.json","state_url":"https://pith.science/pith/HA2XLYDTT66YMILWAR2ETXOZNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HA2XLYDTT66YMILWAR2ETXOZNW/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":"2026-08-21T00:08:22Z","links":{"resolver":"https://pith.science/pith/HA2XLYDTT66YMILWAR2ETXOZNW","bundle":"https://pith.science/pith/HA2XLYDTT66YMILWAR2ETXOZNW/bundle.json","state":"https://pith.science/pith/HA2XLYDTT66YMILWAR2ETXOZNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HA2XLYDTT66YMILWAR2ETXOZNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HA2XLYDTT66YMILWAR2ETXOZNW","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":"4557ee4372a874cdbd7fd784fc1bd90e9e415f0f9040130debb52adbd023ee80","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-20T17:26:08Z","title_canon_sha256":"a6c42b2c52a56fe0add67f41d0a0903ec17db8f7aea6568489eba8a52ea7edff"},"schema_version":"1.0","source":{"id":"2303.11289","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.11289","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"2303.11289v3","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.11289","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"HA2XLYDTT66Y","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_16","alias_value":"HA2XLYDTT66YMILW","created_at":"2026-07-05T10:38:19Z"},{"alias_kind":"pith_short_8","alias_value":"HA2XLYDT","created_at":"2026-07-05T10:38:19Z"}],"graph_snapshots":[{"event_id":"sha256:7c54efdbc2850c95f591c5953b56bed529b126ecd0f7de1dad4718cdbb45f80f","target":"graph","created_at":"2026-07-05T10:38:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.11289/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of deriving a gradient flow structure for the porous medium equation which is {\\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range process with jump rate $g(k)=k^\\alpha, \\alpha>1$ is considered, and its hydrodynamic limit and dynamical large deviations are shown in the presence of both degenerate and unbounded diffusion. The key superexponential estimate is obtained using pathwise discretised regularity estimates in the spirit of the Aubin-Lions-Simons lemma. This allows to exhibit the p","authors_text":"Benjamin Gess, Daniel Heydecker","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-20T17:26:08Z","title":"The Porous Medium Equation: Large Deviations and Gradient Flow with Degenerate and Unbounded Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.11289","kind":"arxiv","version":3},"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":"sha256:1830ba9654a7dc8e571bf28cb6f419377298261b1fd326cce40ecaf3789d7e7b","target":"record","created_at":"2026-07-05T10:38:19Z","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":"4557ee4372a874cdbd7fd784fc1bd90e9e415f0f9040130debb52adbd023ee80","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-20T17:26:08Z","title_canon_sha256":"a6c42b2c52a56fe0add67f41d0a0903ec17db8f7aea6568489eba8a52ea7edff"},"schema_version":"1.0","source":{"id":"2303.11289","kind":"arxiv","version":3}},"canonical_sha256":"383575e0739fbd862176047449ddd96d8d3de34b9c694fb9c8cc02631c8b644a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"383575e0739fbd862176047449ddd96d8d3de34b9c694fb9c8cc02631c8b644a","first_computed_at":"2026-07-05T10:38:19.341694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:38:19.341694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dF1m+VkJOLznTk/ea04Cmd9mO9gG2vUlJTfMrQ3CR9axniDU9h0I1AKbTZDGECboN22XU4UZNd1ZZNANCWfmAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:38:19.342192Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.11289","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1830ba9654a7dc8e571bf28cb6f419377298261b1fd326cce40ecaf3789d7e7b","sha256:7c54efdbc2850c95f591c5953b56bed529b126ecd0f7de1dad4718cdbb45f80f"],"state_sha256":"73e39c3097a818abe403bb0e5cfba5a77f88659990627a0b6d6be0e22a4c5db7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaqHYkzwCtFpR+gH8ib4NIT5vn1WSR925YGHeY1vXOJxPjl9QgjU7jmEjC8UseONVB8JkthiBSvSWSz1J/DHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T00:08:22.344839Z","bundle_sha256":"2140075292c35d3387293ad9efba1680b5b7a040c0374e8335d50843cb1a5819"}}