{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XSJSGSUSRTW35ABKRRXIMVLO76","short_pith_number":"pith:XSJSGSUS","canonical_record":{"source":{"id":"1712.08482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-21T11:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"ac46b63ca98ec879b6157b15807b4e8c94d3c52ade7d5d6b1d16a192efc8b3df","abstract_canon_sha256":"0274cb2daccceb402758b946c1454ee866eab5db1d63e39bc548b0973a8b78e0"},"schema_version":"1.0"},"canonical_sha256":"bc93234a928cedbe802a8c6e86556eff9be35e64cf8447b91b4ac75ad9052495","source":{"kind":"arxiv","id":"1712.08482","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08482","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08482v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08482","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"XSJSGSUSRTW3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XSJSGSUSRTW35ABK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XSJSGSUS","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XSJSGSUSRTW35ABKRRXIMVLO76","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-21T11:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"ac46b63ca98ec879b6157b15807b4e8c94d3c52ade7d5d6b1d16a192efc8b3df","abstract_canon_sha256":"0274cb2daccceb402758b946c1454ee866eab5db1d63e39bc548b0973a8b78e0"},"schema_version":"1.0"},"canonical_sha256":"bc93234a928cedbe802a8c6e86556eff9be35e64cf8447b91b4ac75ad9052495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:23.318838Z","signature_b64":"u88gixSHLC/QwUsvveN/6satvpSDCXwYnGztzQmD75K5TdujKDr2Kxrp0eLJ7TbyryObrDXrcoBV0edzq4vTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc93234a928cedbe802a8c6e86556eff9be35e64cf8447b91b4ac75ad9052495","last_reissued_at":"2026-05-18T00:27:23.318292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:23.318292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08482","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":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7Hj3flNIJA6JH/kjN9rp5jAkON9noxmij2w+7fUu8RTPbsnfYyeAgt/0GK4bUsFK1BMqabV9QWYINjdJ5PPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:14:30.221948Z"},"content_sha256":"d551d41489a251eb2d14fe6a5ec46cea751a0319cc35dfeaa17db7561dd888a2","schema_version":"1.0","event_id":"sha256:d551d41489a251eb2d14fe6a5ec46cea751a0319cc35dfeaa17db7561dd888a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XSJSGSUSRTW35ABKRRXIMVLO76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Encoding Watermark Numbers as Reducible Permutation Graphs using Self-inverting Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Leonidas Palios, Maria Chroni, Stavros D. Nikolopoulos","submitted_at":"2017-12-21T11:10:34Z","abstract_excerpt":"Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper, we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number $w$ as a self-inverting permutation $\\pi^*$, an algorithm for encoding the self-inverting permutation $\\pi^*$ into a reducible permutation graph $F[\\pi^*]$ whose s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08482","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":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NsY73fiJgfy14yLZ42U8X59yD+2Kz32KK11tZv+ZiiMcLOzUAhSBVULMNyOpDlMmRtleRRIpyBkUlXiHHA8xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:14:30.222292Z"},"content_sha256":"68ce2bfa9bb9586ca074ceac857ff0c073f19ac2ea306a29ae7fe2b1e34d16f5","schema_version":"1.0","event_id":"sha256:68ce2bfa9bb9586ca074ceac857ff0c073f19ac2ea306a29ae7fe2b1e34d16f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSJSGSUSRTW35ABKRRXIMVLO76/bundle.json","state_url":"https://pith.science/pith/XSJSGSUSRTW35ABKRRXIMVLO76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSJSGSUSRTW35ABKRRXIMVLO76/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":"2026-06-23T03:14:30Z","links":{"resolver":"https://pith.science/pith/XSJSGSUSRTW35ABKRRXIMVLO76","bundle":"https://pith.science/pith/XSJSGSUSRTW35ABKRRXIMVLO76/bundle.json","state":"https://pith.science/pith/XSJSGSUSRTW35ABKRRXIMVLO76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSJSGSUSRTW35ABKRRXIMVLO76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XSJSGSUSRTW35ABKRRXIMVLO76","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":"0274cb2daccceb402758b946c1454ee866eab5db1d63e39bc548b0973a8b78e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-21T11:10:34Z","title_canon_sha256":"ac46b63ca98ec879b6157b15807b4e8c94d3c52ade7d5d6b1d16a192efc8b3df"},"schema_version":"1.0","source":{"id":"1712.08482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08482","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08482v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08482","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"XSJSGSUSRTW3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XSJSGSUSRTW35ABK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XSJSGSUS","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:68ce2bfa9bb9586ca074ceac857ff0c073f19ac2ea306a29ae7fe2b1e34d16f5","target":"graph","created_at":"2026-05-18T00:27:23Z","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":"Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper, we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number $w$ as a self-inverting permutation $\\pi^*$, an algorithm for encoding the self-inverting permutation $\\pi^*$ into a reducible permutation graph $F[\\pi^*]$ whose s","authors_text":"Leonidas Palios, Maria Chroni, Stavros D. Nikolopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-21T11:10:34Z","title":"Encoding Watermark Numbers as Reducible Permutation Graphs using Self-inverting Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08482","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:d551d41489a251eb2d14fe6a5ec46cea751a0319cc35dfeaa17db7561dd888a2","target":"record","created_at":"2026-05-18T00:27:23Z","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":"0274cb2daccceb402758b946c1454ee866eab5db1d63e39bc548b0973a8b78e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-21T11:10:34Z","title_canon_sha256":"ac46b63ca98ec879b6157b15807b4e8c94d3c52ade7d5d6b1d16a192efc8b3df"},"schema_version":"1.0","source":{"id":"1712.08482","kind":"arxiv","version":1}},"canonical_sha256":"bc93234a928cedbe802a8c6e86556eff9be35e64cf8447b91b4ac75ad9052495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc93234a928cedbe802a8c6e86556eff9be35e64cf8447b91b4ac75ad9052495","first_computed_at":"2026-05-18T00:27:23.318292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:23.318292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u88gixSHLC/QwUsvveN/6satvpSDCXwYnGztzQmD75K5TdujKDr2Kxrp0eLJ7TbyryObrDXrcoBV0edzq4vTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:23.318838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d551d41489a251eb2d14fe6a5ec46cea751a0319cc35dfeaa17db7561dd888a2","sha256:68ce2bfa9bb9586ca074ceac857ff0c073f19ac2ea306a29ae7fe2b1e34d16f5"],"state_sha256":"81fb8f80d884c2b2cc3c815a2d01b04b5853f02118deeff33b9ae4bcc6d8685e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CjfQaKNbZ091ONuyV1i8/LljX1PnQ4gOxeLxqltfLJ1bNKB0Grh8bMkkGs4xZpSCy1OpwyuH6yJf+HAExmfjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:14:30.224387Z","bundle_sha256":"a4a8eb951859f60367a2bdd2019ab36394df0e4350a225eaffcadbf89cd49f3b"}}