{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HLR23BTXSJKC2EPXV6CUVBOB26","short_pith_number":"pith:HLR23BTX","canonical_record":{"source":{"id":"1609.01323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-05T20:57:26Z","cross_cats_sorted":["math.CO","math.CV"],"title_canon_sha256":"9f47a02c390642eb8347ad40564504cf5c25261a6cc9761bb0a1c3504dbced2b","abstract_canon_sha256":"b4d7b5455f545c8e3f5642f04235d314bac9959a6260059c9368f756fc791f54"},"schema_version":"1.0"},"canonical_sha256":"3ae3ad867792542d11f7af854a85c1d7912b7ff297e0b215d1e39efca473f848","source":{"kind":"arxiv","id":"1609.01323","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01323","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01323v1","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01323","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"HLR23BTXSJKC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLR23BTXSJKC2EPX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLR23BTX","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HLR23BTXSJKC2EPXV6CUVBOB26","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-05T20:57:26Z","cross_cats_sorted":["math.CO","math.CV"],"title_canon_sha256":"9f47a02c390642eb8347ad40564504cf5c25261a6cc9761bb0a1c3504dbced2b","abstract_canon_sha256":"b4d7b5455f545c8e3f5642f04235d314bac9959a6260059c9368f756fc791f54"},"schema_version":"1.0"},"canonical_sha256":"3ae3ad867792542d11f7af854a85c1d7912b7ff297e0b215d1e39efca473f848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:41.366330Z","signature_b64":"4HiJjOcL65t4xQjNy56dQ0HotpJuOl61wj59mbF33uGAD0bvfzIrNG0PN2NgU+vdJaxLinOaiLWCHlrLzk5cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ae3ad867792542d11f7af854a85c1d7912b7ff297e0b215d1e39efca473f848","last_reissued_at":"2026-05-18T01:05:41.365837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:41.365837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01323","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":"2026-05-18T01:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFkXzUFCWqgUPXR4iSV0fAxcfyBckbNkziY7bZJsNoRzwy8G1zvG4eYAKByU7c6HGNCgotxL+cSd8k2+vrHiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:29:56.542961Z"},"content_sha256":"b716859db4bd769b2e23846a5d238e63c9c1ba5aaefb68be69f999b764fb5e9e","schema_version":"1.0","event_id":"sha256:b716859db4bd769b2e23846a5d238e63c9c1ba5aaefb68be69f999b764fb5e9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HLR23BTXSJKC2EPXV6CUVBOB26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Newton flows for elliptic functions II Structural stability: Classification & Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CV"],"primary_cat":"math.DS","authors_text":"F. Twilt, G. F. Helminck","submitted_at":"2016-09-05T20:57:26Z","abstract_excerpt":"In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a genericity result. In the present paper we focus on the classification and representation of these structurally stable flows. The phase portrait of a structurally stable elliptic Newton flow generates a connected, cellularly embedded, graph $\\mathcal{G}(f)$ on a torus $T$ with $r$ vertices, 2$r$ edges and $r$ faces that fulfil certain combinatoria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01323","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":"2026-05-18T01:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7agAYF42ztxknaxXH+PfL3/DM7REtfEJOgcH+ZeuoshpvOnBdPBWVBP/khT5WztiG0+Vh2dlGlBXp5FmUZd5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:29:56.543306Z"},"content_sha256":"65c36cef393bf4e4804e9b8848c3e4a08ea1a5f7eaff0eada5cdecc210b85dd7","schema_version":"1.0","event_id":"sha256:65c36cef393bf4e4804e9b8848c3e4a08ea1a5f7eaff0eada5cdecc210b85dd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLR23BTXSJKC2EPXV6CUVBOB26/bundle.json","state_url":"https://pith.science/pith/HLR23BTXSJKC2EPXV6CUVBOB26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLR23BTXSJKC2EPXV6CUVBOB26/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":"2026-06-25T00:29:56Z","links":{"resolver":"https://pith.science/pith/HLR23BTXSJKC2EPXV6CUVBOB26","bundle":"https://pith.science/pith/HLR23BTXSJKC2EPXV6CUVBOB26/bundle.json","state":"https://pith.science/pith/HLR23BTXSJKC2EPXV6CUVBOB26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLR23BTXSJKC2EPXV6CUVBOB26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HLR23BTXSJKC2EPXV6CUVBOB26","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":"b4d7b5455f545c8e3f5642f04235d314bac9959a6260059c9368f756fc791f54","cross_cats_sorted":["math.CO","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-05T20:57:26Z","title_canon_sha256":"9f47a02c390642eb8347ad40564504cf5c25261a6cc9761bb0a1c3504dbced2b"},"schema_version":"1.0","source":{"id":"1609.01323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01323","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01323v1","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01323","created_at":"2026-05-18T01:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"HLR23BTXSJKC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLR23BTXSJKC2EPX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLR23BTX","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:65c36cef393bf4e4804e9b8848c3e4a08ea1a5f7eaff0eada5cdecc210b85dd7","target":"graph","created_at":"2026-05-18T01:05:41Z","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":"In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a genericity result. In the present paper we focus on the classification and representation of these structurally stable flows. The phase portrait of a structurally stable elliptic Newton flow generates a connected, cellularly embedded, graph $\\mathcal{G}(f)$ on a torus $T$ with $r$ vertices, 2$r$ edges and $r$ faces that fulfil certain combinatoria","authors_text":"F. Twilt, G. F. Helminck","cross_cats":["math.CO","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-05T20:57:26Z","title":"Newton flows for elliptic functions II Structural stability: Classification & Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01323","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:b716859db4bd769b2e23846a5d238e63c9c1ba5aaefb68be69f999b764fb5e9e","target":"record","created_at":"2026-05-18T01:05:41Z","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":"b4d7b5455f545c8e3f5642f04235d314bac9959a6260059c9368f756fc791f54","cross_cats_sorted":["math.CO","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-05T20:57:26Z","title_canon_sha256":"9f47a02c390642eb8347ad40564504cf5c25261a6cc9761bb0a1c3504dbced2b"},"schema_version":"1.0","source":{"id":"1609.01323","kind":"arxiv","version":1}},"canonical_sha256":"3ae3ad867792542d11f7af854a85c1d7912b7ff297e0b215d1e39efca473f848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ae3ad867792542d11f7af854a85c1d7912b7ff297e0b215d1e39efca473f848","first_computed_at":"2026-05-18T01:05:41.365837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:41.365837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4HiJjOcL65t4xQjNy56dQ0HotpJuOl61wj59mbF33uGAD0bvfzIrNG0PN2NgU+vdJaxLinOaiLWCHlrLzk5cCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:41.366330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b716859db4bd769b2e23846a5d238e63c9c1ba5aaefb68be69f999b764fb5e9e","sha256:65c36cef393bf4e4804e9b8848c3e4a08ea1a5f7eaff0eada5cdecc210b85dd7"],"state_sha256":"1261f8a949b7e43ee30898c1e12e7a932644f832f8966cfbd9a08a203454e70c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6rgY52/rTiqkG7l77mJw/MOxJ90JMrk7rvRFEZsN3cTDWZAAHDFJ0KvgwOqE3tYycKNiI3KSjITQmc9T3hRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T00:29:56.545353Z","bundle_sha256":"5b31bb0a02d8ff758f6fc2cde1c4d0380384ac71e7f70d0198fc457730b33e99"}}