{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QSD2AB72P6EGH5XWDSOZPTXUAF","short_pith_number":"pith:QSD2AB72","canonical_record":{"source":{"id":"1707.01344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-07-04T02:53:52Z","cross_cats_sorted":["math.CO","q-bio.MN"],"title_canon_sha256":"e888348ada3ffdc143795f82f26801e87a7f03f68cd35b721cd4939724ffde38","abstract_canon_sha256":"ccce0c037dfe1561336ee6f1b86c044aeffd0394efe2515d8dfb93b209df72fb"},"schema_version":"1.0"},"canonical_sha256":"8487a007fa7f8863f6f61c9d97cef401674345183f3513e77a64364db0821fb2","source":{"kind":"arxiv","id":"1707.01344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01344","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01344v1","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01344","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"QSD2AB72P6EG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QSD2AB72P6EGH5XW","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QSD2AB72","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QSD2AB72P6EGH5XWDSOZPTXUAF","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-07-04T02:53:52Z","cross_cats_sorted":["math.CO","q-bio.MN"],"title_canon_sha256":"e888348ada3ffdc143795f82f26801e87a7f03f68cd35b721cd4939724ffde38","abstract_canon_sha256":"ccce0c037dfe1561336ee6f1b86c044aeffd0394efe2515d8dfb93b209df72fb"},"schema_version":"1.0"},"canonical_sha256":"8487a007fa7f8863f6f61c9d97cef401674345183f3513e77a64364db0821fb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.058840Z","signature_b64":"PEHvUqRYlG1Cwcwl6yI5kcQTeJi8heHS2xcABbHZuq1cb68+E6dCSMs8wOAyeWrsaGUr7ctK4ulem06Bn7G6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8487a007fa7f8863f6f61c9d97cef401674345183f3513e77a64364db0821fb2","last_reissued_at":"2026-05-18T00:40:53.058201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.058201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01344","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gnU7oj3e9/zurwaMW9PEdBctdmneZWSQsrhAhZuH6fYso3J3ZoxkxCmhdWBnQ0iwHH4/GQSyBIgWnhaGki6lCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:02:55.789022Z"},"content_sha256":"86c79c810383ca5d9cb7a7f4126728c6214550d80a7a71224f5ee9c10d4df8ad","schema_version":"1.0","event_id":"sha256:86c79c810383ca5d9cb7a7f4126728c6214550d80a7a71224f5ee9c10d4df8ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QSD2AB72P6EGH5XWDSOZPTXUAF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compositions of Functions and Permutations Specified by Minimal Reaction Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","q-bio.MN"],"primary_cat":"cs.FL","authors_text":"Wen Chean Teh","submitted_at":"2017-07-04T02:53:52Z","abstract_excerpt":"This paper studies mathematical properties of reaction systems that was introduced by Enrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the generative power of functions specified by minimal reaction systems under composition initiated by Salomaa. Allowing degenerate reaction systems, functions specified by minimal reaction systems over a quarternary alphabet that are permutations generate the alternating group on the power set of the background set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01344","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2YGp2VIl2v9hRuMIT5dfxUcJGQtZED3UkFfaBoCUNhjl4EdYHOWLHkAERnvNhJ8OzOqibHFXZDvJ2GlubJ/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:02:55.789451Z"},"content_sha256":"94e90ad4e8a17ef7bc6f8fe1cd064bda9936d971cb695e6f66b180c141102aa2","schema_version":"1.0","event_id":"sha256:94e90ad4e8a17ef7bc6f8fe1cd064bda9936d971cb695e6f66b180c141102aa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/bundle.json","state_url":"https://pith.science/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/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":"2026-05-28T00:02:55Z","links":{"resolver":"https://pith.science/pith/QSD2AB72P6EGH5XWDSOZPTXUAF","bundle":"https://pith.science/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/bundle.json","state":"https://pith.science/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSD2AB72P6EGH5XWDSOZPTXUAF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QSD2AB72P6EGH5XWDSOZPTXUAF","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":"ccce0c037dfe1561336ee6f1b86c044aeffd0394efe2515d8dfb93b209df72fb","cross_cats_sorted":["math.CO","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-07-04T02:53:52Z","title_canon_sha256":"e888348ada3ffdc143795f82f26801e87a7f03f68cd35b721cd4939724ffde38"},"schema_version":"1.0","source":{"id":"1707.01344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01344","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01344v1","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01344","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"QSD2AB72P6EG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QSD2AB72P6EGH5XW","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QSD2AB72","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:94e90ad4e8a17ef7bc6f8fe1cd064bda9936d971cb695e6f66b180c141102aa2","target":"graph","created_at":"2026-05-18T00:40:53Z","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 studies mathematical properties of reaction systems that was introduced by Enrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the generative power of functions specified by minimal reaction systems under composition initiated by Salomaa. Allowing degenerate reaction systems, functions specified by minimal reaction systems over a quarternary alphabet that are permutations generate the alternating group on the power set of the background set.","authors_text":"Wen Chean Teh","cross_cats":["math.CO","q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-07-04T02:53:52Z","title":"Compositions of Functions and Permutations Specified by Minimal Reaction Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01344","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":"sha256:86c79c810383ca5d9cb7a7f4126728c6214550d80a7a71224f5ee9c10d4df8ad","target":"record","created_at":"2026-05-18T00:40:53Z","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":"ccce0c037dfe1561336ee6f1b86c044aeffd0394efe2515d8dfb93b209df72fb","cross_cats_sorted":["math.CO","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-07-04T02:53:52Z","title_canon_sha256":"e888348ada3ffdc143795f82f26801e87a7f03f68cd35b721cd4939724ffde38"},"schema_version":"1.0","source":{"id":"1707.01344","kind":"arxiv","version":1}},"canonical_sha256":"8487a007fa7f8863f6f61c9d97cef401674345183f3513e77a64364db0821fb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8487a007fa7f8863f6f61c9d97cef401674345183f3513e77a64364db0821fb2","first_computed_at":"2026-05-18T00:40:53.058201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.058201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PEHvUqRYlG1Cwcwl6yI5kcQTeJi8heHS2xcABbHZuq1cb68+E6dCSMs8wOAyeWrsaGUr7ctK4ulem06Bn7G6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.058840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86c79c810383ca5d9cb7a7f4126728c6214550d80a7a71224f5ee9c10d4df8ad","sha256:94e90ad4e8a17ef7bc6f8fe1cd064bda9936d971cb695e6f66b180c141102aa2"],"state_sha256":"4ed3a5fad2aa9dbf345a155ded28cc3a0ecced146c30ec4ca770d6db5b7ebc0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"030xF8A9GSVKVcVIkWwNXLqo2nrNvjpV0jqG+3xJik6pvghCIifL1rtDIn8m2pJ8T6ehp+aYCI+OwGUhQb3mBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:02:55.792676Z","bundle_sha256":"743f4ae185381e8dd20d9fd21011c719e070168f0319913ac0b2be3230e29a1f"}}