{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7AXE4NRP4NYS4MS4RJGKQYFFGZ","short_pith_number":"pith:7AXE4NRP","canonical_record":{"source":{"id":"1205.3772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2012-05-16T19:49:28Z","cross_cats_sorted":[],"title_canon_sha256":"ce280586bf8db8f7bf54c8395a014d7ff07c4d59e98079813433ae0b23f701e2","abstract_canon_sha256":"b6d56849967d423cbbfdac4d1018dd2e32ba144a87ed1b7662916a30c54f9112"},"schema_version":"1.0"},"canonical_sha256":"f82e4e362fe3712e325c8a4ca860a53651251cf015c4a9f91cdacb0c0236330a","source":{"kind":"arxiv","id":"1205.3772","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3772","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3772v2","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3772","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"7AXE4NRP4NYS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7AXE4NRP4NYS4MS4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7AXE4NRP","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7AXE4NRP4NYS4MS4RJGKQYFFGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2012-05-16T19:49:28Z","cross_cats_sorted":[],"title_canon_sha256":"ce280586bf8db8f7bf54c8395a014d7ff07c4d59e98079813433ae0b23f701e2","abstract_canon_sha256":"b6d56849967d423cbbfdac4d1018dd2e32ba144a87ed1b7662916a30c54f9112"},"schema_version":"1.0"},"canonical_sha256":"f82e4e362fe3712e325c8a4ca860a53651251cf015c4a9f91cdacb0c0236330a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:31.262557Z","signature_b64":"HgjQOE44255Y6stYc6MatCaeRXBNOw0MmlWrSfKxaog8uXzRh01xtYzbx1MNeO4yU6VWmzasVOGni1CbLWnWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f82e4e362fe3712e325c8a4ca860a53651251cf015c4a9f91cdacb0c0236330a","last_reissued_at":"2026-05-18T01:57:31.261963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:31.261963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3772","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":"2026-05-18T01:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ipy90DUT03YMd/TPRygHq0YbiAjG4EHxEaTi4j9J3rZFAuONvN69KSOd5jVpfXgPeiQUNBWI1cpprJyt3RQtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:43:39.461260Z"},"content_sha256":"10686a0d2711478505b904aeeb26371c98063774abc8ea60a5e86a1fb73fb2f7","schema_version":"1.0","event_id":"sha256:10686a0d2711478505b904aeeb26371c98063774abc8ea60a5e86a1fb73fb2f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7AXE4NRP4NYS4MS4RJGKQYFFGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a Rigorous Proof of Magnetism on the Edges of Graphene Nano-ribbons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Hamed Karimi, Ian Affleck","submitted_at":"2012-05-16T19:49:28Z","abstract_excerpt":"A zigzag edge of a graphene nanoribbon supports localized zero modes, ignoring interactions. Based mainly on mean field arguments and numerical approaches, it has been suggested that interactions can produce a large magnetic moment on the edges. By considering the Hubbard model in the weak coupling limit, U<<t, for bearded as well as zigzag edges, we argue for such a magnetic state, based on Lieb's theorem. Projecting the Hubbard interactions onto the flat edge band, we then prove that resulting 1 dimensional model has a fully polarized ferromagnetic ground state. We also study excitons and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3772","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":"2026-05-18T01:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vgq5A5UlRryHw+uLEYj4csYeI8d8EkBDi46PZNKprTVGXgOzKCuzVPrr90A8CahXmtyBS7Q4DsRQyw4cYpl+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:43:39.461992Z"},"content_sha256":"9e43edc7344b6030c66a8c88d6456c4d62e5b446881bcdc8c40005e1b2e2b1dd","schema_version":"1.0","event_id":"sha256:9e43edc7344b6030c66a8c88d6456c4d62e5b446881bcdc8c40005e1b2e2b1dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/bundle.json","state_url":"https://pith.science/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/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":"2026-05-28T17:43:39Z","links":{"resolver":"https://pith.science/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ","bundle":"https://pith.science/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/bundle.json","state":"https://pith.science/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AXE4NRP4NYS4MS4RJGKQYFFGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7AXE4NRP4NYS4MS4RJGKQYFFGZ","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":"b6d56849967d423cbbfdac4d1018dd2e32ba144a87ed1b7662916a30c54f9112","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2012-05-16T19:49:28Z","title_canon_sha256":"ce280586bf8db8f7bf54c8395a014d7ff07c4d59e98079813433ae0b23f701e2"},"schema_version":"1.0","source":{"id":"1205.3772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3772","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3772v2","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3772","created_at":"2026-05-18T01:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"7AXE4NRP4NYS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7AXE4NRP4NYS4MS4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7AXE4NRP","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:9e43edc7344b6030c66a8c88d6456c4d62e5b446881bcdc8c40005e1b2e2b1dd","target":"graph","created_at":"2026-05-18T01:57:31Z","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 zigzag edge of a graphene nanoribbon supports localized zero modes, ignoring interactions. Based mainly on mean field arguments and numerical approaches, it has been suggested that interactions can produce a large magnetic moment on the edges. By considering the Hubbard model in the weak coupling limit, U<<t, for bearded as well as zigzag edges, we argue for such a magnetic state, based on Lieb's theorem. Projecting the Hubbard interactions onto the flat edge band, we then prove that resulting 1 dimensional model has a fully polarized ferromagnetic ground state. We also study excitons and th","authors_text":"Hamed Karimi, Ian Affleck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2012-05-16T19:49:28Z","title":"Towards a Rigorous Proof of Magnetism on the Edges of Graphene Nano-ribbons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3772","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":"sha256:10686a0d2711478505b904aeeb26371c98063774abc8ea60a5e86a1fb73fb2f7","target":"record","created_at":"2026-05-18T01:57:31Z","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":"b6d56849967d423cbbfdac4d1018dd2e32ba144a87ed1b7662916a30c54f9112","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2012-05-16T19:49:28Z","title_canon_sha256":"ce280586bf8db8f7bf54c8395a014d7ff07c4d59e98079813433ae0b23f701e2"},"schema_version":"1.0","source":{"id":"1205.3772","kind":"arxiv","version":2}},"canonical_sha256":"f82e4e362fe3712e325c8a4ca860a53651251cf015c4a9f91cdacb0c0236330a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f82e4e362fe3712e325c8a4ca860a53651251cf015c4a9f91cdacb0c0236330a","first_computed_at":"2026-05-18T01:57:31.261963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:31.261963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HgjQOE44255Y6stYc6MatCaeRXBNOw0MmlWrSfKxaog8uXzRh01xtYzbx1MNeO4yU6VWmzasVOGni1CbLWnWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:31.262557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10686a0d2711478505b904aeeb26371c98063774abc8ea60a5e86a1fb73fb2f7","sha256:9e43edc7344b6030c66a8c88d6456c4d62e5b446881bcdc8c40005e1b2e2b1dd"],"state_sha256":"3b18d70c8fa3d35fc31af75a9f8dfe5b6de4dd33ff4d2cc7a26ab96b403e4468"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBBsiY+wIuxgpqrhYan7A5pVMFxffumRvnWFJo0NMh/zTTeFQ/VxFjALvgKevIWs1Z3pBnwHSxvFpDtjWgiQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:43:39.465596Z","bundle_sha256":"199b2858e3ab416291bb48f6603e43ef216fe9fc75f2037958b1a39f76431d0f"}}