{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:3TF2E2HE7UZF3UNUYBZSU4W4QU","short_pith_number":"pith:3TF2E2HE","canonical_record":{"source":{"id":"math/9301220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1993-01-23T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"43ddfff0d60d31601c0ee4ddac8b593aad9ae69eea19915588174e5bcb808b33","abstract_canon_sha256":"0af5bba74556cda1e3f6743935fda98bcff00deb793e3a1388f3ba66e9ffacb6"},"schema_version":"1.0"},"canonical_sha256":"dccba268e4fd325dd1b4c0732a72dc8522c81066bd152831fa5c7bc36e095d2a","source":{"kind":"arxiv","id":"math/9301220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9301220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9301220v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9301220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"3TF2E2HE7UZF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3TF2E2HE7UZF3UNU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3TF2E2HE","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:3TF2E2HE7UZF3UNUYBZSU4W4QU","target":"record","payload":{"canonical_record":{"source":{"id":"math/9301220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1993-01-23T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"43ddfff0d60d31601c0ee4ddac8b593aad9ae69eea19915588174e5bcb808b33","abstract_canon_sha256":"0af5bba74556cda1e3f6743935fda98bcff00deb793e3a1388f3ba66e9ffacb6"},"schema_version":"1.0"},"canonical_sha256":"dccba268e4fd325dd1b4c0732a72dc8522c81066bd152831fa5c7bc36e095d2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.357044Z","signature_b64":"WXTVPoerGjOgyrWgAZogUl28KKDJ7P0R175BTVifJtC53c6FPt36dT0CBfOfFD/Mm2TraBGa5WRRx70L/JmMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dccba268e4fd325dd1b4c0732a72dc8522c81066bd152831fa5c7bc36e095d2a","last_reissued_at":"2026-05-18T01:05:52.356570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.356570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9301220","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xm0D52XGfr1KVfMRhcjIkRIsJQt29TwNCKYw9T9KkIYovHJF0+RrnuYslLHWrXmO5e5pdLqXcHbBdLltdwY5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T09:16:39.245513Z"},"content_sha256":"a46686eed0a5ed755c74d5da4dab20972b1e5703f8a69340a73f99f0e08efae9","schema_version":"1.0","event_id":"sha256:a46686eed0a5ed755c74d5da4dab20972b1e5703f8a69340a73f99f0e08efae9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:3TF2E2HE7UZF3UNUYBZSU4W4QU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of periodic points of polynomial diffeomorphisms of C^2","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eric Bedford, John Smillie, Mikhail Lyubich","submitted_at":"1993-01-23T00:00:00Z","abstract_excerpt":"This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\\C^2$: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure $\\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9301220","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zeQLhexKfLrKo7H1VHSmPq+IWKyDcClF6QEWTH0EDyojChHL86Sgg3g4D6oy3eQPxlYoHbhV/1a/05xowBX3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T09:16:39.245865Z"},"content_sha256":"ae99f66655732c2019b4dde8572cbc924dfcc63637fe49d4d0ff1e123317ab32","schema_version":"1.0","event_id":"sha256:ae99f66655732c2019b4dde8572cbc924dfcc63637fe49d4d0ff1e123317ab32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/bundle.json","state_url":"https://pith.science/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/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":"2026-06-06T09:16:39Z","links":{"resolver":"https://pith.science/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU","bundle":"https://pith.science/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/bundle.json","state":"https://pith.science/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TF2E2HE7UZF3UNUYBZSU4W4QU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:3TF2E2HE7UZF3UNUYBZSU4W4QU","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":"0af5bba74556cda1e3f6743935fda98bcff00deb793e3a1388f3ba66e9ffacb6","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1993-01-23T00:00:00Z","title_canon_sha256":"43ddfff0d60d31601c0ee4ddac8b593aad9ae69eea19915588174e5bcb808b33"},"schema_version":"1.0","source":{"id":"math/9301220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9301220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9301220v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9301220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"3TF2E2HE7UZF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3TF2E2HE7UZF3UNU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3TF2E2HE","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:ae99f66655732c2019b4dde8572cbc924dfcc63637fe49d4d0ff1e123317ab32","target":"graph","created_at":"2026-05-18T01:05:52Z","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 deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\\C^2$: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure $\\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism","authors_text":"Eric Bedford, John Smillie, Mikhail Lyubich","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1993-01-23T00:00:00Z","title":"Distribution of periodic points of polynomial diffeomorphisms of C^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9301220","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:a46686eed0a5ed755c74d5da4dab20972b1e5703f8a69340a73f99f0e08efae9","target":"record","created_at":"2026-05-18T01:05:52Z","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":"0af5bba74556cda1e3f6743935fda98bcff00deb793e3a1388f3ba66e9ffacb6","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1993-01-23T00:00:00Z","title_canon_sha256":"43ddfff0d60d31601c0ee4ddac8b593aad9ae69eea19915588174e5bcb808b33"},"schema_version":"1.0","source":{"id":"math/9301220","kind":"arxiv","version":1}},"canonical_sha256":"dccba268e4fd325dd1b4c0732a72dc8522c81066bd152831fa5c7bc36e095d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dccba268e4fd325dd1b4c0732a72dc8522c81066bd152831fa5c7bc36e095d2a","first_computed_at":"2026-05-18T01:05:52.356570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.356570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXTVPoerGjOgyrWgAZogUl28KKDJ7P0R175BTVifJtC53c6FPt36dT0CBfOfFD/Mm2TraBGa5WRRx70L/JmMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.357044Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9301220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a46686eed0a5ed755c74d5da4dab20972b1e5703f8a69340a73f99f0e08efae9","sha256:ae99f66655732c2019b4dde8572cbc924dfcc63637fe49d4d0ff1e123317ab32"],"state_sha256":"a0d5c06ea262ec49bacb481c2afc53440cb5c10c509e0145dbf54586ce687074"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWAQzJARzl6uaBZa47Xy4+VWW6jJpHUZUyNX6rweTjutTvF84JUAP3VmvICGJJKcYz9d3FNHfgeOR3ZGv1aWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T09:16:39.248047Z","bundle_sha256":"bbebe078584263a3e593e6d5c1697cb843fa5bf9677d21aad1afc4afa4239a58"}}