{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J3S44CI3CMVOVFAVVTL7LRJHGI","short_pith_number":"pith:J3S44CI3","canonical_record":{"source":{"id":"1512.00802","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T18:34:35Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"34dacc2f058499eb94d38a5c3789039c01235fd408ee2d7609d567aad9353def","abstract_canon_sha256":"43ed80223fe8e023027821bd126b3a9d10854478b75980c5a4fe9856b0e695e8"},"schema_version":"1.0"},"canonical_sha256":"4ee5ce091b132aea9415acd7f5c52732136fd6f33b413d4afbbfbb9622aee9d5","source":{"kind":"arxiv","id":"1512.00802","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00802","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00802v2","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00802","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"J3S44CI3CMVO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J3S44CI3CMVOVFAV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J3S44CI3","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J3S44CI3CMVOVFAVVTL7LRJHGI","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00802","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T18:34:35Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"34dacc2f058499eb94d38a5c3789039c01235fd408ee2d7609d567aad9353def","abstract_canon_sha256":"43ed80223fe8e023027821bd126b3a9d10854478b75980c5a4fe9856b0e695e8"},"schema_version":"1.0"},"canonical_sha256":"4ee5ce091b132aea9415acd7f5c52732136fd6f33b413d4afbbfbb9622aee9d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:06.320139Z","signature_b64":"yu+5kFxoh5KNLSU1iX71yjK4LxYcLrFkEV6k3lZTBbwQubrRGfJN5XTI+DjrDeBhQTw2yi4MPHkqIWPKAKpICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ee5ce091b132aea9415acd7f5c52732136fd6f33b413d4afbbfbb9622aee9d5","last_reissued_at":"2026-05-18T01:20:06.319412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:06.319412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00802","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":"2026-05-18T01:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rb68abmJzBl3ylLmIb02qO6wwvgjbbvoj+UqmbumW29BOpL4aHDQQ8AxsgLufszTu7kE8+LCSefq3cquOp5pBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:15:45.056510Z"},"content_sha256":"321b24677fd1b6145c443a11ca00794ea4c3e130775f97f228eec7c0df705c58","schema_version":"1.0","event_id":"sha256:321b24677fd1b6145c443a11ca00794ea4c3e130775f97f228eec7c0df705c58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J3S44CI3CMVOVFAVVTL7LRJHGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The steady states of coupled dynamical systems compose according to matrix arithmetic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.DS","authors_text":"David I. Spivak","submitted_at":"2015-12-02T18:34:35Z","abstract_excerpt":"Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be arranged in series, in parallel, and with feedback to form a new dynamical system---this is called compositionality---and the process can be repeated in a fractal-like manner to form more complex systems of systems. One issue is that as larger systems are created, their state space grows exponentially.\n  In this paper a technique for calculating the steady states"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00802","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":"2026-05-18T01:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jr1oYqpor0x0131LUaQJSA5tutnS8YsxnTccnyqOM8pLm3G78XpPKsKF+NjSuARtLCa5KaGAIotL1wMuqS8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:15:45.057149Z"},"content_sha256":"99c4dd4231f393a4b8a971d18f651eb1581bee4f5f0da6d51a29f6d5600ea3a5","schema_version":"1.0","event_id":"sha256:99c4dd4231f393a4b8a971d18f651eb1581bee4f5f0da6d51a29f6d5600ea3a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/bundle.json","state_url":"https://pith.science/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/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":"2026-06-08T14:15:45Z","links":{"resolver":"https://pith.science/pith/J3S44CI3CMVOVFAVVTL7LRJHGI","bundle":"https://pith.science/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/bundle.json","state":"https://pith.science/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3S44CI3CMVOVFAVVTL7LRJHGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J3S44CI3CMVOVFAVVTL7LRJHGI","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":"43ed80223fe8e023027821bd126b3a9d10854478b75980c5a4fe9856b0e695e8","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T18:34:35Z","title_canon_sha256":"34dacc2f058499eb94d38a5c3789039c01235fd408ee2d7609d567aad9353def"},"schema_version":"1.0","source":{"id":"1512.00802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00802","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00802v2","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00802","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"J3S44CI3CMVO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J3S44CI3CMVOVFAV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J3S44CI3","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:99c4dd4231f393a4b8a971d18f651eb1581bee4f5f0da6d51a29f6d5600ea3a5","target":"graph","created_at":"2026-05-18T01:20:06Z","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":"Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be arranged in series, in parallel, and with feedback to form a new dynamical system---this is called compositionality---and the process can be repeated in a fractal-like manner to form more complex systems of systems. One issue is that as larger systems are created, their state space grows exponentially.\n  In this paper a technique for calculating the steady states","authors_text":"David I. Spivak","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T18:34:35Z","title":"The steady states of coupled dynamical systems compose according to matrix arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00802","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":"sha256:321b24677fd1b6145c443a11ca00794ea4c3e130775f97f228eec7c0df705c58","target":"record","created_at":"2026-05-18T01:20:06Z","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":"43ed80223fe8e023027821bd126b3a9d10854478b75980c5a4fe9856b0e695e8","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T18:34:35Z","title_canon_sha256":"34dacc2f058499eb94d38a5c3789039c01235fd408ee2d7609d567aad9353def"},"schema_version":"1.0","source":{"id":"1512.00802","kind":"arxiv","version":2}},"canonical_sha256":"4ee5ce091b132aea9415acd7f5c52732136fd6f33b413d4afbbfbb9622aee9d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ee5ce091b132aea9415acd7f5c52732136fd6f33b413d4afbbfbb9622aee9d5","first_computed_at":"2026-05-18T01:20:06.319412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:06.319412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yu+5kFxoh5KNLSU1iX71yjK4LxYcLrFkEV6k3lZTBbwQubrRGfJN5XTI+DjrDeBhQTw2yi4MPHkqIWPKAKpICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:06.320139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:321b24677fd1b6145c443a11ca00794ea4c3e130775f97f228eec7c0df705c58","sha256:99c4dd4231f393a4b8a971d18f651eb1581bee4f5f0da6d51a29f6d5600ea3a5"],"state_sha256":"bcfe70d85a67d9ee52936590ab87561788efa7fea22e3e8d871927f98630c7c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQgukuFqcdoX3/tqb4qvdynknJTYVpW96QjZP37snmzPmzFmuQLp1mfvNrH8SyXM3zl7e6EJ6AwThRubNVzzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:15:45.060424Z","bundle_sha256":"b4bcc99ea94730e050f0fc369be250f7ab33cda7479d0c0587399e27b429159b"}}