{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:R56D27TK2JPQZSCYY42Q6QQOML","short_pith_number":"pith:R56D27TK","canonical_record":{"source":{"id":"1512.00267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-12-01T14:23:16Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"1ae96c8fc14b408a7672b19c28072605704cbd32d98925623ef7ab898ac99a46","abstract_canon_sha256":"2cd53b70e1a976dc4026d4ba7de16435bd4db87aa62c1e69c6a1a4bc61babf6c"},"schema_version":"1.0"},"canonical_sha256":"8f7c3d7e6ad25f0cc858c7350f420e62cbcb8600f4237066a4919daa889b4a20","source":{"kind":"arxiv","id":"1512.00267","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00267","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00267v2","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00267","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"R56D27TK2JPQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R56D27TK2JPQZSCY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R56D27TK","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:R56D27TK2JPQZSCYY42Q6QQOML","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-12-01T14:23:16Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"1ae96c8fc14b408a7672b19c28072605704cbd32d98925623ef7ab898ac99a46","abstract_canon_sha256":"2cd53b70e1a976dc4026d4ba7de16435bd4db87aa62c1e69c6a1a4bc61babf6c"},"schema_version":"1.0"},"canonical_sha256":"8f7c3d7e6ad25f0cc858c7350f420e62cbcb8600f4237066a4919daa889b4a20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:57.865254Z","signature_b64":"sO9SSpqAj8xe44vMW7lRXvJQeaYbCWbIAYVhpo5uB4EiE7BbSo+YxB0P/tfHxxu8GO7XWTg9uZV9pP//K/FJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f7c3d7e6ad25f0cc858c7350f420e62cbcb8600f4237066a4919daa889b4a20","last_reissued_at":"2026-05-18T01:15:57.864532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:57.864532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00267","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":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aL7H89kg+nFSHT0qiGeEJn9157yAz3mxHu2npkGoTzCDyyRSGTKmOKkKkVHveTg5uq4UOizyCpQPfYEMkX9dBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:28:14.127003Z"},"content_sha256":"122905ec18cf79d7a947abff5d247f4bbd67cf5c902d55825d9852894e3fefd3","schema_version":"1.0","event_id":"sha256:122905ec18cf79d7a947abff5d247f4bbd67cf5c902d55825d9852894e3fefd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:R56D27TK2JPQZSCYY42Q6QQOML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.MN"],"primary_cat":"math.MG","authors_text":"Georg Regensburger, Stefan M\\\"uller","submitted_at":"2015-12-01T14:23:16Z","abstract_excerpt":"A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community.\n  Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00267","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":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQBmQ6GbI90otKSZU4NfCklSzofNxhgV4DX5943i9PS7p+DGuYc2sWTAS4f5JO2745iaZRBO13ssy1oiaODqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:28:14.127768Z"},"content_sha256":"68388fd1f3f1d6540e724f9a06b134fff38981f6acac995edd87f3924876903d","schema_version":"1.0","event_id":"sha256:68388fd1f3f1d6540e724f9a06b134fff38981f6acac995edd87f3924876903d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R56D27TK2JPQZSCYY42Q6QQOML/bundle.json","state_url":"https://pith.science/pith/R56D27TK2JPQZSCYY42Q6QQOML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R56D27TK2JPQZSCYY42Q6QQOML/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":"2026-05-23T12:28:14Z","links":{"resolver":"https://pith.science/pith/R56D27TK2JPQZSCYY42Q6QQOML","bundle":"https://pith.science/pith/R56D27TK2JPQZSCYY42Q6QQOML/bundle.json","state":"https://pith.science/pith/R56D27TK2JPQZSCYY42Q6QQOML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R56D27TK2JPQZSCYY42Q6QQOML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:R56D27TK2JPQZSCYY42Q6QQOML","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":"2cd53b70e1a976dc4026d4ba7de16435bd4db87aa62c1e69c6a1a4bc61babf6c","cross_cats_sorted":["q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-12-01T14:23:16Z","title_canon_sha256":"1ae96c8fc14b408a7672b19c28072605704cbd32d98925623ef7ab898ac99a46"},"schema_version":"1.0","source":{"id":"1512.00267","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00267","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00267v2","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00267","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"R56D27TK2JPQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R56D27TK2JPQZSCY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R56D27TK","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:68388fd1f3f1d6540e724f9a06b134fff38981f6acac995edd87f3924876903d","target":"graph","created_at":"2026-05-18T01:15:57Z","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":"A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community.\n  Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear su","authors_text":"Georg Regensburger, Stefan M\\\"uller","cross_cats":["q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-12-01T14:23:16Z","title":"Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00267","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":"sha256:122905ec18cf79d7a947abff5d247f4bbd67cf5c902d55825d9852894e3fefd3","target":"record","created_at":"2026-05-18T01:15:57Z","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":"2cd53b70e1a976dc4026d4ba7de16435bd4db87aa62c1e69c6a1a4bc61babf6c","cross_cats_sorted":["q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-12-01T14:23:16Z","title_canon_sha256":"1ae96c8fc14b408a7672b19c28072605704cbd32d98925623ef7ab898ac99a46"},"schema_version":"1.0","source":{"id":"1512.00267","kind":"arxiv","version":2}},"canonical_sha256":"8f7c3d7e6ad25f0cc858c7350f420e62cbcb8600f4237066a4919daa889b4a20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f7c3d7e6ad25f0cc858c7350f420e62cbcb8600f4237066a4919daa889b4a20","first_computed_at":"2026-05-18T01:15:57.864532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:57.864532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sO9SSpqAj8xe44vMW7lRXvJQeaYbCWbIAYVhpo5uB4EiE7BbSo+YxB0P/tfHxxu8GO7XWTg9uZV9pP//K/FJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:57.865254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00267","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:122905ec18cf79d7a947abff5d247f4bbd67cf5c902d55825d9852894e3fefd3","sha256:68388fd1f3f1d6540e724f9a06b134fff38981f6acac995edd87f3924876903d"],"state_sha256":"1fb953bc7719b70bfef0e41b10d8a18ec2977074034f934a2153fbb20414fa7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91nGDgKCVHesUwY4OHd6euWBk++nwBw22vpw2Q8JXZxwIeoHCo98W5qpe5kk1zmgb0ScS18cpz6nmzY5T8RZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T12:28:14.132093Z","bundle_sha256":"9947afd74ca1b594c8402297a5b681a4ba6c71c22b2908834c57ab654f5b1ae0"}}