{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IU2DH5BNSNGPXHL532ISRAZ7X3","short_pith_number":"pith:IU2DH5BN","canonical_record":{"source":{"id":"1512.00779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-12-02T17:23:50Z","cross_cats_sorted":[],"title_canon_sha256":"ee408502c15be16429678aec028eb27293311cbd3db5365978f6c57ea13c0c37","abstract_canon_sha256":"33120a8fba44cb2cff43393c99b4b411b0e4507b781d6f40fa7299f72599d294"},"schema_version":"1.0"},"canonical_sha256":"453433f42d934cfb9d7dde9128833fbed16ebf939f04db85c22aad1bbf5a8469","source":{"kind":"arxiv","id":"1512.00779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00779","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00779v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00779","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"IU2DH5BNSNGP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IU2DH5BNSNGPXHL5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IU2DH5BN","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IU2DH5BNSNGPXHL532ISRAZ7X3","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-12-02T17:23:50Z","cross_cats_sorted":[],"title_canon_sha256":"ee408502c15be16429678aec028eb27293311cbd3db5365978f6c57ea13c0c37","abstract_canon_sha256":"33120a8fba44cb2cff43393c99b4b411b0e4507b781d6f40fa7299f72599d294"},"schema_version":"1.0"},"canonical_sha256":"453433f42d934cfb9d7dde9128833fbed16ebf939f04db85c22aad1bbf5a8469","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:25.105541Z","signature_b64":"5Vo2Xe+3fYSOWfZRTAVVCvmzvefbsQzYns9OKvzHeGB+gKkQmZ5aNjzqosGc6DXjf53lzAsMGR0Q2f1iwX6yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"453433f42d934cfb9d7dde9128833fbed16ebf939f04db85c22aad1bbf5a8469","last_reissued_at":"2026-05-18T01:25:25.104880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:25.104880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00779","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":"2026-05-18T01:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AebqGjyWCvQxE58Rey3hW5mGy4hHFtyk+z7kHgNcVAuviEZRq/4vJvDOzxie+sNSJqJuqD1DuviDizvJ6NX/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:56:38.250433Z"},"content_sha256":"593416f0de2a92505237d19368cfd01ff099a1dff0b93376ab96113092f77810","schema_version":"1.0","event_id":"sha256:593416f0de2a92505237d19368cfd01ff099a1dff0b93376ab96113092f77810"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IU2DH5BNSNGPXHL532ISRAZ7X3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dipole Codes Attractively Encode Glue Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Andrew Winslow, Dhananjay Ipparthi, Massimo Mastrangeli","submitted_at":"2015-12-02T17:23:50Z","abstract_excerpt":"Dipole words are sequences of magnetic dipoles, in which alike elements repel and opposite elements attract. Magnetic dipoles contrast with more general sets of bonding types, called glues, in which pairwise bonding strength is specified by a glue function. We prove that every glue function $g$ has a set of dipole words, called a dipole code, that attractively encodes $g$: the pairwise attractions (positive or non-positive bond strength) between the words are identical to those of $g$. Moreover, we give such word sets of asymptotically optimal length. Similar results are obtained for a commonl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00779","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":"2026-05-18T01:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrDSRld5OySgardAu3PD+vA1cKHcHlFUmrUVvw2bjGeGTna7WQasdkicx73rIlEpK0loXBu+c2cgn2dXk8nVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:56:38.250776Z"},"content_sha256":"0fdbf5f16a3a99758ed812e17c3db6d48160903c48368af6258e27796f387f57","schema_version":"1.0","event_id":"sha256:0fdbf5f16a3a99758ed812e17c3db6d48160903c48368af6258e27796f387f57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/bundle.json","state_url":"https://pith.science/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/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":"2026-06-23T16:56:38Z","links":{"resolver":"https://pith.science/pith/IU2DH5BNSNGPXHL532ISRAZ7X3","bundle":"https://pith.science/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/bundle.json","state":"https://pith.science/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IU2DH5BNSNGPXHL532ISRAZ7X3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IU2DH5BNSNGPXHL532ISRAZ7X3","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":"33120a8fba44cb2cff43393c99b4b411b0e4507b781d6f40fa7299f72599d294","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-12-02T17:23:50Z","title_canon_sha256":"ee408502c15be16429678aec028eb27293311cbd3db5365978f6c57ea13c0c37"},"schema_version":"1.0","source":{"id":"1512.00779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00779","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00779v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00779","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"IU2DH5BNSNGP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IU2DH5BNSNGPXHL5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IU2DH5BN","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:0fdbf5f16a3a99758ed812e17c3db6d48160903c48368af6258e27796f387f57","target":"graph","created_at":"2026-05-18T01:25:25Z","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":"Dipole words are sequences of magnetic dipoles, in which alike elements repel and opposite elements attract. Magnetic dipoles contrast with more general sets of bonding types, called glues, in which pairwise bonding strength is specified by a glue function. We prove that every glue function $g$ has a set of dipole words, called a dipole code, that attractively encodes $g$: the pairwise attractions (positive or non-positive bond strength) between the words are identical to those of $g$. Moreover, we give such word sets of asymptotically optimal length. Similar results are obtained for a commonl","authors_text":"Andrew Winslow, Dhananjay Ipparthi, Massimo Mastrangeli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-12-02T17:23:50Z","title":"Dipole Codes Attractively Encode Glue Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00779","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":"sha256:593416f0de2a92505237d19368cfd01ff099a1dff0b93376ab96113092f77810","target":"record","created_at":"2026-05-18T01:25:25Z","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":"33120a8fba44cb2cff43393c99b4b411b0e4507b781d6f40fa7299f72599d294","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-12-02T17:23:50Z","title_canon_sha256":"ee408502c15be16429678aec028eb27293311cbd3db5365978f6c57ea13c0c37"},"schema_version":"1.0","source":{"id":"1512.00779","kind":"arxiv","version":1}},"canonical_sha256":"453433f42d934cfb9d7dde9128833fbed16ebf939f04db85c22aad1bbf5a8469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"453433f42d934cfb9d7dde9128833fbed16ebf939f04db85c22aad1bbf5a8469","first_computed_at":"2026-05-18T01:25:25.104880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:25.104880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Vo2Xe+3fYSOWfZRTAVVCvmzvefbsQzYns9OKvzHeGB+gKkQmZ5aNjzqosGc6DXjf53lzAsMGR0Q2f1iwX6yDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:25.105541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:593416f0de2a92505237d19368cfd01ff099a1dff0b93376ab96113092f77810","sha256:0fdbf5f16a3a99758ed812e17c3db6d48160903c48368af6258e27796f387f57"],"state_sha256":"d79a64ec307959b1800901c4009c74587967701d9218039718164fc25249922e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipa9PondBvrlf4IvTdL8xAyykiyOQshPtT+7KBH2bSfrAHsgruIdcXRGSepOc2CC9MlFJVjiNJgcQWC++aF3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:56:38.252679Z","bundle_sha256":"fa8a7a0d6ebcd109c6ff661b64cc3a348b8757f20c6c6979f3235a42c39ef06b"}}