{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BX4UVIPR5KAQIVXXIWWVFSEV77","short_pith_number":"pith:BX4UVIPR","canonical_record":{"source":{"id":"1908.08448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-22T15:25:19Z","cross_cats_sorted":["math.IT","math.RA"],"title_canon_sha256":"cda9960ebbaf3810bef1c99d4663d7dae5e4d5141c94b74dac48a89f024d7883","abstract_canon_sha256":"d8a1d13fadf1256bbc687ad99a2fa7b0855f08f16451cfabd6716e2e9d57204a"},"schema_version":"1.0"},"canonical_sha256":"0df94aa1f1ea810456f745ad52c895fff50e84094cd6d3ec4cb5219a24373df0","source":{"kind":"arxiv","id":"1908.08448","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08448","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08448v2","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08448","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"BX4UVIPR5KAQ","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"BX4UVIPR5KAQIVXX","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"BX4UVIPR","created_at":"2026-07-05T00:05:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BX4UVIPR5KAQIVXXIWWVFSEV77","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-22T15:25:19Z","cross_cats_sorted":["math.IT","math.RA"],"title_canon_sha256":"cda9960ebbaf3810bef1c99d4663d7dae5e4d5141c94b74dac48a89f024d7883","abstract_canon_sha256":"d8a1d13fadf1256bbc687ad99a2fa7b0855f08f16451cfabd6716e2e9d57204a"},"schema_version":"1.0"},"canonical_sha256":"0df94aa1f1ea810456f745ad52c895fff50e84094cd6d3ec4cb5219a24373df0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:05:45.948671Z","signature_b64":"L0wooDqJHpoTferDahQ3+EOT5G575fq0jG1TOVmhT9XTUK/Q+vaTSFNfvE6SNPJkGCqtHeMQIHPeGT8FZVmICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df94aa1f1ea810456f745ad52c895fff50e84094cd6d3ec4cb5219a24373df0","last_reissued_at":"2026-07-05T00:05:45.948165Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:05:45.948165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08448","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":"2026-07-05T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xy+3RZg40nHv1RsAhmMRu5uTXC5wRVhQPLC2QklkKimbFOiy+kMzDoZoGw7VwaqhykHh03yM7bH5d8Ah67GRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:11:24.411370Z"},"content_sha256":"aa1bafd14b2e19bc7768c2b52b2b0b5201aeb913c2e1802c5ac7dca4a2e5fe6d","schema_version":"1.0","event_id":"sha256:aa1bafd14b2e19bc7768c2b52b2b0b5201aeb913c2e1802c5ac7dca4a2e5fe6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BX4UVIPR5KAQIVXXIWWVFSEV77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine equivalence for quadratic rotation symmetric Boolean functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Alexandru Chirvasitu, Thomas W. Cusick","submitted_at":"2019-08-22T15:25:19Z","abstract_excerpt":"Let $f_n(x_0, x_1, \\ldots, x_{n-1})$ denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree $d$ in $n \\geq d$ variables and let $wt(f_n)$ denote the Hamming weight of this function. Let $(0, a_1, \\ldots, a_{d-1})_n$ denote the function $f_n$ of degree $d$ in $n$ variables generated by the monomial $x_0x_{a_1} \\cdots x_{a_{d-1}}.$ Such a function $f_n$ is called monomial rotation symmetric (MRS). It was proved in a $2012$ paper that for any MRS $f_n$ with $d=3,$ the sequence of weights $\\{w_k = wt(f_k):~k = 3, 4, \\ldots\\}$ satisfies a homogene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08448","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08448/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wx8s3rUv6r9Ym49oyTsKeBX34ZUla0/ynzZ9J3GZJUWhsqvDMh5acFcngeYJ9jOWtWiXy7/sCCUY91zeZFEjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:11:24.411965Z"},"content_sha256":"95248a2fe5925ac70ccd0022bab930f5114699a433199ecaca8bebeb0cfbb472","schema_version":"1.0","event_id":"sha256:95248a2fe5925ac70ccd0022bab930f5114699a433199ecaca8bebeb0cfbb472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/bundle.json","state_url":"https://pith.science/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/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":"2026-08-16T18:11:24Z","links":{"resolver":"https://pith.science/pith/BX4UVIPR5KAQIVXXIWWVFSEV77","bundle":"https://pith.science/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/bundle.json","state":"https://pith.science/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BX4UVIPR5KAQIVXXIWWVFSEV77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BX4UVIPR5KAQIVXXIWWVFSEV77","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":"d8a1d13fadf1256bbc687ad99a2fa7b0855f08f16451cfabd6716e2e9d57204a","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-22T15:25:19Z","title_canon_sha256":"cda9960ebbaf3810bef1c99d4663d7dae5e4d5141c94b74dac48a89f024d7883"},"schema_version":"1.0","source":{"id":"1908.08448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08448","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08448v2","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08448","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"BX4UVIPR5KAQ","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"BX4UVIPR5KAQIVXX","created_at":"2026-07-05T00:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"BX4UVIPR","created_at":"2026-07-05T00:05:45Z"}],"graph_snapshots":[{"event_id":"sha256:95248a2fe5925ac70ccd0022bab930f5114699a433199ecaca8bebeb0cfbb472","target":"graph","created_at":"2026-07-05T00:05:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f_n(x_0, x_1, \\ldots, x_{n-1})$ denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree $d$ in $n \\geq d$ variables and let $wt(f_n)$ denote the Hamming weight of this function. Let $(0, a_1, \\ldots, a_{d-1})_n$ denote the function $f_n$ of degree $d$ in $n$ variables generated by the monomial $x_0x_{a_1} \\cdots x_{a_{d-1}}.$ Such a function $f_n$ is called monomial rotation symmetric (MRS). It was proved in a $2012$ paper that for any MRS $f_n$ with $d=3,$ the sequence of weights $\\{w_k = wt(f_k):~k = 3, 4, \\ldots\\}$ satisfies a homogene","authors_text":"Alexandru Chirvasitu, Thomas W. Cusick","cross_cats":["math.IT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-22T15:25:19Z","title":"Affine equivalence for quadratic rotation symmetric Boolean functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08448","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:aa1bafd14b2e19bc7768c2b52b2b0b5201aeb913c2e1802c5ac7dca4a2e5fe6d","target":"record","created_at":"2026-07-05T00:05:45Z","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":"d8a1d13fadf1256bbc687ad99a2fa7b0855f08f16451cfabd6716e2e9d57204a","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-22T15:25:19Z","title_canon_sha256":"cda9960ebbaf3810bef1c99d4663d7dae5e4d5141c94b74dac48a89f024d7883"},"schema_version":"1.0","source":{"id":"1908.08448","kind":"arxiv","version":2}},"canonical_sha256":"0df94aa1f1ea810456f745ad52c895fff50e84094cd6d3ec4cb5219a24373df0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0df94aa1f1ea810456f745ad52c895fff50e84094cd6d3ec4cb5219a24373df0","first_computed_at":"2026-07-05T00:05:45.948165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:05:45.948165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L0wooDqJHpoTferDahQ3+EOT5G575fq0jG1TOVmhT9XTUK/Q+vaTSFNfvE6SNPJkGCqtHeMQIHPeGT8FZVmICw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:05:45.948671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa1bafd14b2e19bc7768c2b52b2b0b5201aeb913c2e1802c5ac7dca4a2e5fe6d","sha256:95248a2fe5925ac70ccd0022bab930f5114699a433199ecaca8bebeb0cfbb472"],"state_sha256":"67d93794586d082560bb7b7b77935b014154d4c969664973128718dd6b01aff2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yfui0n3OdXYwRxp3TS8HNzwpRpM0BrcjAQWnJTPbXiVfRCVy5VBIKFMIKiQhOda2j47wMQ3ORmJfQSh6m2PRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:11:24.416183Z","bundle_sha256":"88522648d1fc9084b2e45c517939ee32873b7a4aa9146d4ff7f17768d0712029"}}