{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RVI44BK2XKZK5BR6AV7BW4K4CH","short_pith_number":"pith:RVI44BK2","canonical_record":{"source":{"id":"1412.5216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-16T22:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"d3d72b1c33b71db7a5ab0cba02c4e0c68401535306410b295f83b4373f8d5e82","abstract_canon_sha256":"e9d728065f2dc72c87969dac2d01386f62305fcec1f084e726a79970635f73c4"},"schema_version":"1.0"},"canonical_sha256":"8d51ce055abab2ae863e057e1b715c11c1618b76122a6138049fef67b80bbc2d","source":{"kind":"arxiv","id":"1412.5216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5216","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5216v1","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5216","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"RVI44BK2XKZK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RVI44BK2XKZK5BR6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RVI44BK2","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RVI44BK2XKZK5BR6AV7BW4K4CH","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-16T22:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"d3d72b1c33b71db7a5ab0cba02c4e0c68401535306410b295f83b4373f8d5e82","abstract_canon_sha256":"e9d728065f2dc72c87969dac2d01386f62305fcec1f084e726a79970635f73c4"},"schema_version":"1.0"},"canonical_sha256":"8d51ce055abab2ae863e057e1b715c11c1618b76122a6138049fef67b80bbc2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:41.553238Z","signature_b64":"cWVMXyzuNKU5dekt7vnLpieAWHUNEIRYKo+ZGGw8slKwZ7fNdeSGG1gDUW7KgtVcsRrbR66VNfN/Z5FHa+DdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d51ce055abab2ae863e057e1b715c11c1618b76122a6138049fef67b80bbc2d","last_reissued_at":"2026-05-18T01:22:41.552789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:41.552789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5216","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":"2026-05-18T01:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5fry5VfnnVTWXSbyDjKwpmhrCzyXlrSiCcYwAG1XplpwtbVN/PEQt37lWdliQj2C9zoNLak8/VWaVz+inIiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:20:48.812947Z"},"content_sha256":"49870cd0c99793f3f1c6ab41b972cb888aa83cfbad65207cc4048d66281f17cf","schema_version":"1.0","event_id":"sha256:49870cd0c99793f3f1c6ab41b972cb888aa83cfbad65207cc4048d66281f17cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RVI44BK2XKZK5BR6AV7BW4K4CH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Advection of Methane in the Hydrate Zone: Model, Analysis and Examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Justin T. Webster, Malgorzata Peszynska, Ralph E. Showalter","submitted_at":"2014-12-16T22:27:52Z","abstract_excerpt":"A two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique generalized solution in $L^1$; the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach space for an m-accretive multi-valued operator. Additional estimates of maximum principle type are obtained, and these permit appropriate maximal extensions of the phase-change relations. An example with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5216","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":"2026-05-18T01:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHPz1Z7G1lx8euVxfrRUNiXiwFHNmvR2BnUXSYvZwhkgfBuzuJ6xK6RGreTRTbJ8k2DZsZuJu9tphZ92ss5rAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:20:48.813453Z"},"content_sha256":"e1d25cd29c8292c399bc22d8e8bf1dbf3a0e4941b475c5e472d3594b78470e39","schema_version":"1.0","event_id":"sha256:e1d25cd29c8292c399bc22d8e8bf1dbf3a0e4941b475c5e472d3594b78470e39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/bundle.json","state_url":"https://pith.science/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/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":"2026-06-03T21:20:48Z","links":{"resolver":"https://pith.science/pith/RVI44BK2XKZK5BR6AV7BW4K4CH","bundle":"https://pith.science/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/bundle.json","state":"https://pith.science/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVI44BK2XKZK5BR6AV7BW4K4CH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RVI44BK2XKZK5BR6AV7BW4K4CH","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":"e9d728065f2dc72c87969dac2d01386f62305fcec1f084e726a79970635f73c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-16T22:27:52Z","title_canon_sha256":"d3d72b1c33b71db7a5ab0cba02c4e0c68401535306410b295f83b4373f8d5e82"},"schema_version":"1.0","source":{"id":"1412.5216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5216","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5216v1","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5216","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"RVI44BK2XKZK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RVI44BK2XKZK5BR6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RVI44BK2","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:e1d25cd29c8292c399bc22d8e8bf1dbf3a0e4941b475c5e472d3594b78470e39","target":"graph","created_at":"2026-05-18T01:22:41Z","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 two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique generalized solution in $L^1$; the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach space for an m-accretive multi-valued operator. Additional estimates of maximum principle type are obtained, and these permit appropriate maximal extensions of the phase-change relations. An example with","authors_text":"Justin T. Webster, Malgorzata Peszynska, Ralph E. Showalter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-16T22:27:52Z","title":"Advection of Methane in the Hydrate Zone: Model, Analysis and Examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5216","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":"sha256:49870cd0c99793f3f1c6ab41b972cb888aa83cfbad65207cc4048d66281f17cf","target":"record","created_at":"2026-05-18T01:22:41Z","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":"e9d728065f2dc72c87969dac2d01386f62305fcec1f084e726a79970635f73c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-16T22:27:52Z","title_canon_sha256":"d3d72b1c33b71db7a5ab0cba02c4e0c68401535306410b295f83b4373f8d5e82"},"schema_version":"1.0","source":{"id":"1412.5216","kind":"arxiv","version":1}},"canonical_sha256":"8d51ce055abab2ae863e057e1b715c11c1618b76122a6138049fef67b80bbc2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d51ce055abab2ae863e057e1b715c11c1618b76122a6138049fef67b80bbc2d","first_computed_at":"2026-05-18T01:22:41.552789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:41.552789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWVMXyzuNKU5dekt7vnLpieAWHUNEIRYKo+ZGGw8slKwZ7fNdeSGG1gDUW7KgtVcsRrbR66VNfN/Z5FHa+DdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:41.553238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49870cd0c99793f3f1c6ab41b972cb888aa83cfbad65207cc4048d66281f17cf","sha256:e1d25cd29c8292c399bc22d8e8bf1dbf3a0e4941b475c5e472d3594b78470e39"],"state_sha256":"29afcf3705bc4315d40b8c9c002730d6a9c7717698ae18c607592800ae3959b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILJOgjqqJGIsfSHJX6xtJRAJfDy0cSb/OTe6iqsMTtoP42eBev5rIkvPiqgWT1k8j5JdENThXo0QjYtIejUsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:20:48.815689Z","bundle_sha256":"25eeca17237e23fc9205d56fb981784b4771c6ab0ab8d167d8c21db9f8d03df6"}}