{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KPUISQTP7VQSFM2BRSM47KVB3W","short_pith_number":"pith:KPUISQTP","canonical_record":{"source":{"id":"1503.04688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-16T15:29:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9b15ebc1afc05e90c54502b7eac1478d9c3617251977f80a5f2ce3ac906f9ebd","abstract_canon_sha256":"66f9b4217ad29da4aaeabfee0f61bb7c17d5bc52df0aafd35494b877c4bbfdfc"},"schema_version":"1.0"},"canonical_sha256":"53e889426ffd6122b3418c99cfaaa1ddb7358b5028a762e01f9388188dfb0caa","source":{"kind":"arxiv","id":"1503.04688","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04688","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04688v2","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04688","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"KPUISQTP7VQS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPUISQTP7VQSFM2B","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPUISQTP","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KPUISQTP7VQSFM2BRSM47KVB3W","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-16T15:29:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9b15ebc1afc05e90c54502b7eac1478d9c3617251977f80a5f2ce3ac906f9ebd","abstract_canon_sha256":"66f9b4217ad29da4aaeabfee0f61bb7c17d5bc52df0aafd35494b877c4bbfdfc"},"schema_version":"1.0"},"canonical_sha256":"53e889426ffd6122b3418c99cfaaa1ddb7358b5028a762e01f9388188dfb0caa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:30.381183Z","signature_b64":"CKGLF0YIejJJyT8e7AcJBnYCWmDuKwAUtdZclITeTGJQJs8rA5a0f18+pkR/yeSY0jcwCPeKaeCXvwChIdeUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53e889426ffd6122b3418c99cfaaa1ddb7358b5028a762e01f9388188dfb0caa","last_reissued_at":"2026-05-18T01:19:30.380598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:30.380598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04688","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":"2026-05-18T01:19:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KYZOV/0zmSzRa5AE+HxTO+G8khFw+S0ZdYs2WCKMUoWP9AZVO7c8PjTvDtp0z6kCCSToCvZNQo2WEgW34ObAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:15:28.065547Z"},"content_sha256":"e90b7c8af98d38a47197529603cbb313f76d4c8bff1825a1ca2d167f94680dfc","schema_version":"1.0","event_id":"sha256:e90b7c8af98d38a47197529603cbb313f76d4c8bff1825a1ca2d167f94680dfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KPUISQTP7VQSFM2BRSM47KVB3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple dynamics on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Adrien Richard, Maximilien Gadouleau","submitted_at":"2015-03-16T15:29:46Z","abstract_excerpt":"Does the interaction graph of a finite dynamical system can force this system to have a \"complex\" dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system $f:A^n\\to A^n$ with $G$ as interaction graph has a \"complex\" dynamics ? If $|A|\\geq 3$ we prove that no such signed digraph exists. More precisely, we prove that for every signed digraph $G$ there exists a system $f:A^n\\to A^n$ with $G$ as interaction graph that converges toward a unique fixed point in at most $\\lfloor\\log_2 n\\rfloor+2$ steps. The boolean ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04688","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":"2026-05-18T01:19:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uMsrlFDII9tp0s34dKhCLm/c/cmkEWjdFsqnrDiUXTxlKVXAwkOb/1dwdfEQtHy2EEuU0SKRGX1mpIp/qxI0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:15:28.065892Z"},"content_sha256":"c1af0dcc29a5b8fc13a8694d83826dcfb46e2fe2354483cf85365f199c60733e","schema_version":"1.0","event_id":"sha256:c1af0dcc29a5b8fc13a8694d83826dcfb46e2fe2354483cf85365f199c60733e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPUISQTP7VQSFM2BRSM47KVB3W/bundle.json","state_url":"https://pith.science/pith/KPUISQTP7VQSFM2BRSM47KVB3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPUISQTP7VQSFM2BRSM47KVB3W/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":"2026-07-02T21:15:28Z","links":{"resolver":"https://pith.science/pith/KPUISQTP7VQSFM2BRSM47KVB3W","bundle":"https://pith.science/pith/KPUISQTP7VQSFM2BRSM47KVB3W/bundle.json","state":"https://pith.science/pith/KPUISQTP7VQSFM2BRSM47KVB3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPUISQTP7VQSFM2BRSM47KVB3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KPUISQTP7VQSFM2BRSM47KVB3W","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":"66f9b4217ad29da4aaeabfee0f61bb7c17d5bc52df0aafd35494b877c4bbfdfc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-16T15:29:46Z","title_canon_sha256":"9b15ebc1afc05e90c54502b7eac1478d9c3617251977f80a5f2ce3ac906f9ebd"},"schema_version":"1.0","source":{"id":"1503.04688","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04688","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04688v2","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04688","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"KPUISQTP7VQS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPUISQTP7VQSFM2B","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPUISQTP","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:c1af0dcc29a5b8fc13a8694d83826dcfb46e2fe2354483cf85365f199c60733e","target":"graph","created_at":"2026-05-18T01:19:30Z","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":"Does the interaction graph of a finite dynamical system can force this system to have a \"complex\" dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system $f:A^n\\to A^n$ with $G$ as interaction graph has a \"complex\" dynamics ? If $|A|\\geq 3$ we prove that no such signed digraph exists. More precisely, we prove that for every signed digraph $G$ there exists a system $f:A^n\\to A^n$ with $G$ as interaction graph that converges toward a unique fixed point in at most $\\lfloor\\log_2 n\\rfloor+2$ steps. The boolean ca","authors_text":"Adrien Richard, Maximilien Gadouleau","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-16T15:29:46Z","title":"Simple dynamics on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04688","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:e90b7c8af98d38a47197529603cbb313f76d4c8bff1825a1ca2d167f94680dfc","target":"record","created_at":"2026-05-18T01:19:30Z","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":"66f9b4217ad29da4aaeabfee0f61bb7c17d5bc52df0aafd35494b877c4bbfdfc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-16T15:29:46Z","title_canon_sha256":"9b15ebc1afc05e90c54502b7eac1478d9c3617251977f80a5f2ce3ac906f9ebd"},"schema_version":"1.0","source":{"id":"1503.04688","kind":"arxiv","version":2}},"canonical_sha256":"53e889426ffd6122b3418c99cfaaa1ddb7358b5028a762e01f9388188dfb0caa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53e889426ffd6122b3418c99cfaaa1ddb7358b5028a762e01f9388188dfb0caa","first_computed_at":"2026-05-18T01:19:30.380598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:30.380598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CKGLF0YIejJJyT8e7AcJBnYCWmDuKwAUtdZclITeTGJQJs8rA5a0f18+pkR/yeSY0jcwCPeKaeCXvwChIdeUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:30.381183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04688","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e90b7c8af98d38a47197529603cbb313f76d4c8bff1825a1ca2d167f94680dfc","sha256:c1af0dcc29a5b8fc13a8694d83826dcfb46e2fe2354483cf85365f199c60733e"],"state_sha256":"39cfa1b5d122980759774feafdee5ef6e011f78ac84afe8db786326064a9a77a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2sP/JPBrB1iRy5u9wBauYG0v552mH9h9g9RNfUXisQ+oo4kWXGLtNCvDrRST0AKTtjbtuGbPJYPlMGV1R3gBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:15:28.067809Z","bundle_sha256":"f3e8a4f96d8d029cf05c7bfe859b32d8109ffbdc5355cfc3d8eee3a57ea48585"}}