{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O6UAOIUCADKQ2OHGI3QIXG4SD3","short_pith_number":"pith:O6UAOIUC","canonical_record":{"source":{"id":"1304.1723","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-05T14:22:50Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"d5398b610d4eddd4cd05a7ec2b5f8b11ac2c8417e4c86d63650f0aafb901d0b9","abstract_canon_sha256":"9a587e5be7bd70cbbeeff4e686d427a99182408fbced670bca3880446e527e49"},"schema_version":"1.0"},"canonical_sha256":"77a807228200d50d38e646e08b9b921ed64f87994fee624487de1a9289534f8d","source":{"kind":"arxiv","id":"1304.1723","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1723","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1723v3","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1723","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"O6UAOIUCADKQ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6UAOIUCADKQ2OHG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6UAOIUC","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O6UAOIUCADKQ2OHGI3QIXG4SD3","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1723","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-05T14:22:50Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"d5398b610d4eddd4cd05a7ec2b5f8b11ac2c8417e4c86d63650f0aafb901d0b9","abstract_canon_sha256":"9a587e5be7bd70cbbeeff4e686d427a99182408fbced670bca3880446e527e49"},"schema_version":"1.0"},"canonical_sha256":"77a807228200d50d38e646e08b9b921ed64f87994fee624487de1a9289534f8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:26.627459Z","signature_b64":"l/co6/CKQYgiXllxZDs4yDAX+NqwxgRgWJlT6xEKECSW3qedwZBOEXfcH8ChZM3w+cWu9iPYZSBDgkApJMzFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77a807228200d50d38e646e08b9b921ed64f87994fee624487de1a9289534f8d","last_reissued_at":"2026-05-18T03:10:26.626725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:26.626725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1723","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":"2026-05-18T03:10:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P1U8RyEIoXqTb8tLjolMQQehkxVlMClIuyv0lVcR+pD5qvrAMSemIW3gCjcrN1a54DJRr4gESmOeZyD/D5t/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:30:01.419346Z"},"content_sha256":"631bdc9c45c40d272775e53775f8d2b626e1c9f141268ff8136b26b916fc4b07","schema_version":"1.0","event_id":"sha256:631bdc9c45c40d272775e53775f8d2b626e1c9f141268ff8136b26b916fc4b07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O6UAOIUCADKQ2OHGI3QIXG4SD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg Reaction-Diffusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.DS","authors_text":"Daniel Wetzel, Hannes Uecker","submitted_at":"2013-04-05T14:22:50Z","abstract_excerpt":"For a Selkov--Schnakenberg model as a prototype reaction-diffusion system on two dimensional domains we use the continuation and bifurcation software pde2path to numerically calculate branches of patterns embedded in patterns, for instance hexagons embedded in stripes and vice versa, with a planar interface between the two patterns. We use the Ginzburg-Landau reduction to approximate the locations of these branches by Maxwell points for the associated Ginzburg-Landau system. For our basic model, some but not all of these branches show a snaking behaviour in parameter space, over the given comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1723","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":""},"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":"2026-05-18T03:10:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7WpJMgg02Q55YzgY1bVX2UCNSbnupmtzsTNhDBJw8F74zDlmmEo8AuiF5sYCzWh+8TfGU6vcBQfiivQf9YTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:30:01.419713Z"},"content_sha256":"af22197f13848f6e238eb24d1810b9e3bc61338aed070a4dd13bb2d813a5795a","schema_version":"1.0","event_id":"sha256:af22197f13848f6e238eb24d1810b9e3bc61338aed070a4dd13bb2d813a5795a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/bundle.json","state_url":"https://pith.science/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/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":"2026-06-04T18:30:01Z","links":{"resolver":"https://pith.science/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3","bundle":"https://pith.science/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/bundle.json","state":"https://pith.science/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6UAOIUCADKQ2OHGI3QIXG4SD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O6UAOIUCADKQ2OHGI3QIXG4SD3","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":"9a587e5be7bd70cbbeeff4e686d427a99182408fbced670bca3880446e527e49","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-05T14:22:50Z","title_canon_sha256":"d5398b610d4eddd4cd05a7ec2b5f8b11ac2c8417e4c86d63650f0aafb901d0b9"},"schema_version":"1.0","source":{"id":"1304.1723","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1723","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1723v3","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1723","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"O6UAOIUCADKQ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6UAOIUCADKQ2OHG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6UAOIUC","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:af22197f13848f6e238eb24d1810b9e3bc61338aed070a4dd13bb2d813a5795a","target":"graph","created_at":"2026-05-18T03:10:26Z","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":"For a Selkov--Schnakenberg model as a prototype reaction-diffusion system on two dimensional domains we use the continuation and bifurcation software pde2path to numerically calculate branches of patterns embedded in patterns, for instance hexagons embedded in stripes and vice versa, with a planar interface between the two patterns. We use the Ginzburg-Landau reduction to approximate the locations of these branches by Maxwell points for the associated Ginzburg-Landau system. For our basic model, some but not all of these branches show a snaking behaviour in parameter space, over the given comp","authors_text":"Daniel Wetzel, Hannes Uecker","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-05T14:22:50Z","title":"Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg Reaction-Diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1723","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":"sha256:631bdc9c45c40d272775e53775f8d2b626e1c9f141268ff8136b26b916fc4b07","target":"record","created_at":"2026-05-18T03:10:26Z","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":"9a587e5be7bd70cbbeeff4e686d427a99182408fbced670bca3880446e527e49","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-05T14:22:50Z","title_canon_sha256":"d5398b610d4eddd4cd05a7ec2b5f8b11ac2c8417e4c86d63650f0aafb901d0b9"},"schema_version":"1.0","source":{"id":"1304.1723","kind":"arxiv","version":3}},"canonical_sha256":"77a807228200d50d38e646e08b9b921ed64f87994fee624487de1a9289534f8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a807228200d50d38e646e08b9b921ed64f87994fee624487de1a9289534f8d","first_computed_at":"2026-05-18T03:10:26.626725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:26.626725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/co6/CKQYgiXllxZDs4yDAX+NqwxgRgWJlT6xEKECSW3qedwZBOEXfcH8ChZM3w+cWu9iPYZSBDgkApJMzFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:26.627459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1723","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:631bdc9c45c40d272775e53775f8d2b626e1c9f141268ff8136b26b916fc4b07","sha256:af22197f13848f6e238eb24d1810b9e3bc61338aed070a4dd13bb2d813a5795a"],"state_sha256":"aedafbf011e43a42de76730e7ee0a8b9f0b5bae36ad57273fc26e5f1b0e77191"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaR6wSC9UE8Gjclw3IVhpT6+8vd5c8NEONtvMFdwldHi7Gp6hv4X8fObys/VkD66slZQlXnH8JBOZhD+T9k5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:30:01.421775Z","bundle_sha256":"3f86b5be8f19afdc22c433268f207e4e4de9810e94db93d52a38a067eb68f4c9"}}