{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WMDN4KSUKWJRSC6TUJBPBIXYYA","short_pith_number":"pith:WMDN4KSU","canonical_record":{"source":{"id":"1602.02399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-07T18:10:45Z","cross_cats_sorted":[],"title_canon_sha256":"43485de28200384d60cdcfb7e54e484a0522639ca24c3b4efb51808106bb0503","abstract_canon_sha256":"74b9925c72bb816a151ba6bae15231e90525788dafb0701a3da4bf7037797476"},"schema_version":"1.0"},"canonical_sha256":"b306de2a545593190bd3a242f0a2f8c03d9083e8c99aea6fd454ae904af92a9e","source":{"kind":"arxiv","id":"1602.02399","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02399","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02399v1","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02399","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"WMDN4KSUKWJR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WMDN4KSUKWJRSC6T","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WMDN4KSU","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WMDN4KSUKWJRSC6TUJBPBIXYYA","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-07T18:10:45Z","cross_cats_sorted":[],"title_canon_sha256":"43485de28200384d60cdcfb7e54e484a0522639ca24c3b4efb51808106bb0503","abstract_canon_sha256":"74b9925c72bb816a151ba6bae15231e90525788dafb0701a3da4bf7037797476"},"schema_version":"1.0"},"canonical_sha256":"b306de2a545593190bd3a242f0a2f8c03d9083e8c99aea6fd454ae904af92a9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:10.097888Z","signature_b64":"CSno3B9tFGhCKQqIc2sgrn+gRa2eAwzMwEUiwU1OCxJ1CxbfQfSxZWomstL0r8doozgt6LskywP75YPZb9uEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b306de2a545593190bd3a242f0a2f8c03d9083e8c99aea6fd454ae904af92a9e","last_reissued_at":"2026-05-18T01:21:10.097240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:10.097240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02399","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":"2026-05-18T01:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3lCVf10cC/AL6pGVtUS3r12aUvGuM92eVFIWLuzoJfPCM/wOxmqNDMa3hRvcRRN049YfcM2R/Yf8SrG9J96BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:20:02.547754Z"},"content_sha256":"1a5f356e81bd36d5abc2c17cbc554cd61f0a5b362b27dc6e46fc031a5d9fa0a7","schema_version":"1.0","event_id":"sha256:1a5f356e81bd36d5abc2c17cbc554cd61f0a5b362b27dc6e46fc031a5d9fa0a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WMDN4KSUKWJRSC6TUJBPBIXYYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chains of compact cylinders for cusp-generic nearly integrable convex systems on $\\mathbb{A}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Pierre Marco","submitted_at":"2016-02-07T18:10:45Z","abstract_excerpt":"This paper is the first of a series of three dedicated to a proof of the Arnold diffusion conjecture for perturbations of {convex} integrable Hamiltonian systems on $\\mathbb{A}^3=\\mathbb{T}^3\\times \\mathbb{R}^3$.\n  We consider systems of the form $H(\\theta,r)=h(r)+f(\\theta,r)$, where $h$ is a $C^\\kappa$ strictly convex and superlinear function on $\\mathbb{R}^3$ and $f\\in C^\\kappa(\\mathbb{A}^3)$, $\\kappa\\geq2$. Given $e>\\textrm{{Min}}\\,h$ and a finite family of arbitrary open sets $O_i$ in $\\mathbb{R}^3$ intersecting $h^{-1}(e)$, a diffusion orbit associated with these data is an orbit of $H$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02399","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":"2026-05-18T01:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwTuU5kr56iFcdzesK0nxcuvCFGwqST9huRXTlbCN4/4MVyFU1xLKtSkNcUiySORogDY1JHVV6aBSoC5RTQlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:20:02.548361Z"},"content_sha256":"8daec41eccd6f7cc726918f5cef61f50c4de91bd1a4b99fa75dab82993356eef","schema_version":"1.0","event_id":"sha256:8daec41eccd6f7cc726918f5cef61f50c4de91bd1a4b99fa75dab82993356eef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/bundle.json","state_url":"https://pith.science/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/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":"2026-07-01T07:20:02Z","links":{"resolver":"https://pith.science/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA","bundle":"https://pith.science/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/bundle.json","state":"https://pith.science/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMDN4KSUKWJRSC6TUJBPBIXYYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WMDN4KSUKWJRSC6TUJBPBIXYYA","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":"74b9925c72bb816a151ba6bae15231e90525788dafb0701a3da4bf7037797476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-07T18:10:45Z","title_canon_sha256":"43485de28200384d60cdcfb7e54e484a0522639ca24c3b4efb51808106bb0503"},"schema_version":"1.0","source":{"id":"1602.02399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02399","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02399v1","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02399","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"WMDN4KSUKWJR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WMDN4KSUKWJRSC6T","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WMDN4KSU","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:8daec41eccd6f7cc726918f5cef61f50c4de91bd1a4b99fa75dab82993356eef","target":"graph","created_at":"2026-05-18T01:21:10Z","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":"This paper is the first of a series of three dedicated to a proof of the Arnold diffusion conjecture for perturbations of {convex} integrable Hamiltonian systems on $\\mathbb{A}^3=\\mathbb{T}^3\\times \\mathbb{R}^3$.\n  We consider systems of the form $H(\\theta,r)=h(r)+f(\\theta,r)$, where $h$ is a $C^\\kappa$ strictly convex and superlinear function on $\\mathbb{R}^3$ and $f\\in C^\\kappa(\\mathbb{A}^3)$, $\\kappa\\geq2$. Given $e>\\textrm{{Min}}\\,h$ and a finite family of arbitrary open sets $O_i$ in $\\mathbb{R}^3$ intersecting $h^{-1}(e)$, a diffusion orbit associated with these data is an orbit of $H$ w","authors_text":"Jean-Pierre Marco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-07T18:10:45Z","title":"Chains of compact cylinders for cusp-generic nearly integrable convex systems on $\\mathbb{A}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02399","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":"sha256:1a5f356e81bd36d5abc2c17cbc554cd61f0a5b362b27dc6e46fc031a5d9fa0a7","target":"record","created_at":"2026-05-18T01:21:10Z","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":"74b9925c72bb816a151ba6bae15231e90525788dafb0701a3da4bf7037797476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-07T18:10:45Z","title_canon_sha256":"43485de28200384d60cdcfb7e54e484a0522639ca24c3b4efb51808106bb0503"},"schema_version":"1.0","source":{"id":"1602.02399","kind":"arxiv","version":1}},"canonical_sha256":"b306de2a545593190bd3a242f0a2f8c03d9083e8c99aea6fd454ae904af92a9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b306de2a545593190bd3a242f0a2f8c03d9083e8c99aea6fd454ae904af92a9e","first_computed_at":"2026-05-18T01:21:10.097240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:10.097240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CSno3B9tFGhCKQqIc2sgrn+gRa2eAwzMwEUiwU1OCxJ1CxbfQfSxZWomstL0r8doozgt6LskywP75YPZb9uEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:10.097888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a5f356e81bd36d5abc2c17cbc554cd61f0a5b362b27dc6e46fc031a5d9fa0a7","sha256:8daec41eccd6f7cc726918f5cef61f50c4de91bd1a4b99fa75dab82993356eef"],"state_sha256":"899521c1d353a24eba9b5130067965e429293e485898cc8249ee95a2817321b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1+pETW759pOJCm+vOtjCFImo+p/WFBxyzO+/sfh6OoRekUgx26HO5YJlAW6ll8cpac0nQ+paqsihwJtwA5eAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:20:02.550715Z","bundle_sha256":"d9eacf850aab395ed8562f765866828d6f8ec683b340897576fecc6667e86453"}}