{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AH43TGJWKNKH43F4ONKWG6AGHE","short_pith_number":"pith:AH43TGJW","canonical_record":{"source":{"id":"1611.01909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-07T06:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"6e48d0da12066922bffc32788c106d67b266425511ec4b585eb653d14ab448ce","abstract_canon_sha256":"c1662bf14fa74e5e3566521bae7f7c36d31c2698f9ce20f023b97cf34615d2d6"},"schema_version":"1.0"},"canonical_sha256":"01f9b9993653547e6cbc7355637806393e569cdeef2a8d10dc3b77cedb334d0e","source":{"kind":"arxiv","id":"1611.01909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01909","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01909v1","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01909","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"pith_short_12","alias_value":"AH43TGJWKNKH","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AH43TGJWKNKH43F4","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AH43TGJW","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AH43TGJWKNKH43F4ONKWG6AGHE","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-07T06:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"6e48d0da12066922bffc32788c106d67b266425511ec4b585eb653d14ab448ce","abstract_canon_sha256":"c1662bf14fa74e5e3566521bae7f7c36d31c2698f9ce20f023b97cf34615d2d6"},"schema_version":"1.0"},"canonical_sha256":"01f9b9993653547e6cbc7355637806393e569cdeef2a8d10dc3b77cedb334d0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:04.192712Z","signature_b64":"gijxIV17pT807tvAvqW7ymPG7zoEWp/OCJk4dbfZzrfRbONvA8FViBFN2sfzN6egeY6Bo7f87KmwCsYHDLWPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01f9b9993653547e6cbc7355637806393e569cdeef2a8d10dc3b77cedb334d0e","last_reissued_at":"2026-05-18T01:00:04.191974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:04.191974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01909","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":"2026-05-18T01:00:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9TfFyAiGpqERZ2qxqd4DJzxGvqxgoMenPuJnUIWENTE5G8tUs68hsaCPQz3TOAzzXI47z4pDpuQgaTfbDXCyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:06:06.565433Z"},"content_sha256":"65a7b260e6c11cc1743b6b84ac260761b6b720c89e04b22287039af035923890","schema_version":"1.0","event_id":"sha256:65a7b260e6c11cc1743b6b84ac260761b6b720c89e04b22287039af035923890"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AH43TGJWKNKH43F4ONKWG6AGHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Weiwei Ding, Xing Liang, Yihong Du","submitted_at":"2016-11-07T06:43:44Z","abstract_excerpt":"We aim to classify the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. In time-periodic and space homogeneous environment, as well as in space-periodic and time autonomous environment, such a problem has been studied recently in \\cite{dgp, dl}. In both cases, a spreading-vanishing dichotomy has been established, and when spreading happens, the asymptotic spreading speed is proved to ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01909","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":"2026-05-18T01:00:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GviOHl+ZPx4kNcRn3+TzrMDIhgrHQEofbt+j6FDOS3QedhukYCPPb43U3HUEGVpDUOobXOdxFV6nlXOO8OM+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:06:06.565785Z"},"content_sha256":"1eb31021d9f1ae40c4976d9131a93c65fd89969cee3d7691ed809d218427c27b","schema_version":"1.0","event_id":"sha256:1eb31021d9f1ae40c4976d9131a93c65fd89969cee3d7691ed809d218427c27b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AH43TGJWKNKH43F4ONKWG6AGHE/bundle.json","state_url":"https://pith.science/pith/AH43TGJWKNKH43F4ONKWG6AGHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AH43TGJWKNKH43F4ONKWG6AGHE/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":"2026-06-02T00:06:06Z","links":{"resolver":"https://pith.science/pith/AH43TGJWKNKH43F4ONKWG6AGHE","bundle":"https://pith.science/pith/AH43TGJWKNKH43F4ONKWG6AGHE/bundle.json","state":"https://pith.science/pith/AH43TGJWKNKH43F4ONKWG6AGHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AH43TGJWKNKH43F4ONKWG6AGHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AH43TGJWKNKH43F4ONKWG6AGHE","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":"c1662bf14fa74e5e3566521bae7f7c36d31c2698f9ce20f023b97cf34615d2d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-07T06:43:44Z","title_canon_sha256":"6e48d0da12066922bffc32788c106d67b266425511ec4b585eb653d14ab448ce"},"schema_version":"1.0","source":{"id":"1611.01909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01909","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01909v1","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01909","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"pith_short_12","alias_value":"AH43TGJWKNKH","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AH43TGJWKNKH43F4","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AH43TGJW","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:1eb31021d9f1ae40c4976d9131a93c65fd89969cee3d7691ed809d218427c27b","target":"graph","created_at":"2026-05-18T01:00:04Z","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 aim to classify the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. In time-periodic and space homogeneous environment, as well as in space-periodic and time autonomous environment, such a problem has been studied recently in \\cite{dgp, dl}. In both cases, a spreading-vanishing dichotomy has been established, and when spreading happens, the asymptotic spreading speed is proved to ex","authors_text":"Weiwei Ding, Xing Liang, Yihong Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-07T06:43:44Z","title":"Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01909","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":"sha256:65a7b260e6c11cc1743b6b84ac260761b6b720c89e04b22287039af035923890","target":"record","created_at":"2026-05-18T01:00:04Z","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":"c1662bf14fa74e5e3566521bae7f7c36d31c2698f9ce20f023b97cf34615d2d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-07T06:43:44Z","title_canon_sha256":"6e48d0da12066922bffc32788c106d67b266425511ec4b585eb653d14ab448ce"},"schema_version":"1.0","source":{"id":"1611.01909","kind":"arxiv","version":1}},"canonical_sha256":"01f9b9993653547e6cbc7355637806393e569cdeef2a8d10dc3b77cedb334d0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01f9b9993653547e6cbc7355637806393e569cdeef2a8d10dc3b77cedb334d0e","first_computed_at":"2026-05-18T01:00:04.191974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:04.191974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gijxIV17pT807tvAvqW7ymPG7zoEWp/OCJk4dbfZzrfRbONvA8FViBFN2sfzN6egeY6Bo7f87KmwCsYHDLWPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:04.192712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65a7b260e6c11cc1743b6b84ac260761b6b720c89e04b22287039af035923890","sha256:1eb31021d9f1ae40c4976d9131a93c65fd89969cee3d7691ed809d218427c27b"],"state_sha256":"aa30eeb2b8fc6e85daf83eb3d302a352eccb5837e468ad50b9b652c6c0ff68ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/gQJgtVB7Z4zYBneMkXK9LDQphiLUymlWfDEiN08xf5FHHRyV7N66UvgHfZUIEEENU7UcSUQ/iaWVHTVcYMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:06:06.567792Z","bundle_sha256":"e1feacf8cf72938b4947073cb30c8efd899d0d599d18e5d15655cc5c199c89f2"}}