{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PN7TSXFIUVSJ633JEBAFNM7GTE","short_pith_number":"pith:PN7TSXFI","canonical_record":{"source":{"id":"1110.2710","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-12T17:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"67e9e68b198c5c93a348a0110bdc3c4f1563748aa5618fb7c0f1ebab85989847","abstract_canon_sha256":"2990804fd789b73bb4596ccc2cc29ab5771008e600c0969d85d47c4b53ad1e8d"},"schema_version":"1.0"},"canonical_sha256":"7b7f395ca8a5649f6f69204056b3e699150c1ad20492d2470d3deb269a17324b","source":{"kind":"arxiv","id":"1110.2710","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2710","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2710v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2710","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"PN7TSXFIUVSJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PN7TSXFIUVSJ633J","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PN7TSXFI","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PN7TSXFIUVSJ633JEBAFNM7GTE","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2710","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-12T17:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"67e9e68b198c5c93a348a0110bdc3c4f1563748aa5618fb7c0f1ebab85989847","abstract_canon_sha256":"2990804fd789b73bb4596ccc2cc29ab5771008e600c0969d85d47c4b53ad1e8d"},"schema_version":"1.0"},"canonical_sha256":"7b7f395ca8a5649f6f69204056b3e699150c1ad20492d2470d3deb269a17324b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:34.701712Z","signature_b64":"0XDbOHjM3ASLayZAc0g2Mqe3+9lP0ysr+gqUswY2kdZ/IztWPH+t4YMuNFp9p0w9J3cMJ1pnNTCbmr2ElF+fDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b7f395ca8a5649f6f69204056b3e699150c1ad20492d2470d3deb269a17324b","last_reissued_at":"2026-05-18T00:55:34.701301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:34.701301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2710","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJfSqEjSXuZHVz/NKhECfjetgP7VVMzTa3IWJ4/pJmW3Pg42zjbg+MoflK3Fi6xbuE+TNBYsfVx7q6i1rI9WAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:22:50.880433Z"},"content_sha256":"1e5f8881b434c2d66c8151424a877b1e7f5932687eb02c02b0aeb673c90528b3","schema_version":"1.0","event_id":"sha256:1e5f8881b434c2d66c8151424a877b1e7f5932687eb02c02b0aeb673c90528b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PN7TSXFIUVSJ633JEBAFNM7GTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bego\\~na Alarc\\'on, Isabel S. Labouriau, Sofia B. S. D. Castro","submitted_at":"2011-10-12T17:14:51Z","abstract_excerpt":"We probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the Discrete Markus-Yamabe Question are those possessing Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2710","kind":"arxiv","version":2},"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":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRLSDU1vmwRXi4qiAmm2hDOVeZF9+gnQv5k2ArlLsUCfafJHBzpS68VSBEsaGeK5g3Zr3w1IDyySDk6juYl7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:22:50.880978Z"},"content_sha256":"769834242f44b0d562dbf5ca7293b1ca0aa1e17232096cc62f2ff3a559ffe321","schema_version":"1.0","event_id":"sha256:769834242f44b0d562dbf5ca7293b1ca0aa1e17232096cc62f2ff3a559ffe321"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/bundle.json","state_url":"https://pith.science/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/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":"2026-06-08T11:22:50Z","links":{"resolver":"https://pith.science/pith/PN7TSXFIUVSJ633JEBAFNM7GTE","bundle":"https://pith.science/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/bundle.json","state":"https://pith.science/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PN7TSXFIUVSJ633JEBAFNM7GTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PN7TSXFIUVSJ633JEBAFNM7GTE","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":"2990804fd789b73bb4596ccc2cc29ab5771008e600c0969d85d47c4b53ad1e8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-12T17:14:51Z","title_canon_sha256":"67e9e68b198c5c93a348a0110bdc3c4f1563748aa5618fb7c0f1ebab85989847"},"schema_version":"1.0","source":{"id":"1110.2710","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2710","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2710v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2710","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"PN7TSXFIUVSJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PN7TSXFIUVSJ633J","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PN7TSXFI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:769834242f44b0d562dbf5ca7293b1ca0aa1e17232096cc62f2ff3a559ffe321","target":"graph","created_at":"2026-05-18T00:55:34Z","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 probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the Discrete Markus-Yamabe Question are those possessing Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map.","authors_text":"Bego\\~na Alarc\\'on, Isabel S. Labouriau, Sofia B. S. D. Castro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-12T17:14:51Z","title":"The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2710","kind":"arxiv","version":2},"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":"sha256:1e5f8881b434c2d66c8151424a877b1e7f5932687eb02c02b0aeb673c90528b3","target":"record","created_at":"2026-05-18T00:55:34Z","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":"2990804fd789b73bb4596ccc2cc29ab5771008e600c0969d85d47c4b53ad1e8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-12T17:14:51Z","title_canon_sha256":"67e9e68b198c5c93a348a0110bdc3c4f1563748aa5618fb7c0f1ebab85989847"},"schema_version":"1.0","source":{"id":"1110.2710","kind":"arxiv","version":2}},"canonical_sha256":"7b7f395ca8a5649f6f69204056b3e699150c1ad20492d2470d3deb269a17324b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7f395ca8a5649f6f69204056b3e699150c1ad20492d2470d3deb269a17324b","first_computed_at":"2026-05-18T00:55:34.701301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:34.701301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0XDbOHjM3ASLayZAc0g2Mqe3+9lP0ysr+gqUswY2kdZ/IztWPH+t4YMuNFp9p0w9J3cMJ1pnNTCbmr2ElF+fDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:34.701712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2710","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e5f8881b434c2d66c8151424a877b1e7f5932687eb02c02b0aeb673c90528b3","sha256:769834242f44b0d562dbf5ca7293b1ca0aa1e17232096cc62f2ff3a559ffe321"],"state_sha256":"95a59ab798e53e610d5efc57c3446d4652ed6c5e6ea978c3e07058d8782fdd48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZqWwzVm2zBheG85w+8JenLyiMk1IqAIPT7mC3hOevl9VVb69AnWPRAr/xUuCMEPjBVpTQ0hb/2Ipy/imjJmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T11:22:50.883084Z","bundle_sha256":"8c062a6f09445993273b04d18573986fe75773cb342e9eaf619d08796d8e9253"}}